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Override for the tutor's lesson content generation calls. Auto uses the system default (Claude Sonnet 5 for lesson text, Opus 5 for diagrams).

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Tutoring abilities

Have you ever seen a clear ruler shaped like a rainbow or half a cookie?

This special tool is called a **protractor**, and it measures how wide corners open up.

<!DOCTYPE html>
<html lang="en">
<head>
  <meta charset="UTF-8">
  <meta name="viewport" content="width=device-width, initial-scale=1.0">
  <meta name="aspect-ratio" content="4:3">
  <title>Parts of a Protractor</title>
  <style>
    * { box-sizing: border-box; margin: 0; padding: 0; }
    body {
      font-family: -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, sans-serif;
      background: transparent;
      color: #1e2945;
      display: flex;
      flex-direction: column;
      align-items: center;
      justify-content: space-between;
      min-height: 100%;
      padding: 8px;
      user-select: none;
      -webkit-user-select: none;
    }

    .btn-group {
      display: flex;
      flex-wrap: wrap;
      gap: 6px;
      justify-content: center;
      width: 100%;
      max-width: 520px;
      margin-bottom: 6px;
    }

    .btn {
      appearance: none;
      border: 1.5px solid #e2e8f0;
      background: #ffffff;
      color: #475569;
      padding: 6px 12px;
      font-size: 13px;
      font-weight: 600;
      border-radius: 20px;
      cursor: pointer;
      display: inline-flex;
      align-items: center;
      gap: 5px;
      transition: background-color 0.2s, color 0.2s, box-shadow 0.2s, border-color 0.2s;
    }

    .btn:active { transform: translateY(1px); }
    .btn.active {
      background: #1e2945;
      color: #ffffff;
      border-color: #1e2945;
      box-shadow: 0 2px 6px rgba(30, 41, 69, 0.25);
    }

    .dot-indicator {
      width: 8px;
      height: 8px;
      border-radius: 50%;
      display: inline-block;
    }

    .protractor-container {
      position: relative;
      width: 100%;
      max-width: 500px;
      aspect-ratio: 500 / 270;
      display: flex;
      align-items: center;
      justify-content: center;
    }

    svg {
      width: 100%;
      height: 100%;
      overflow: visible;
    }

    /* Interactive spotlight highlights */
    .part {
      transition: opacity 0.3s ease, stroke 0.3s ease;
    }

    .dimmed {
      opacity: 0.15 !important;
    }

    .highlight-outer {
      stroke: #0284c7 !important;
      fill: #0284c7 !important;
      font-weight: 700;
    }

    .highlight-inner {
      stroke: #d946ef !important;
      fill: #d946ef !important;
      font-weight: 700;
    }

    .highlight-base {
      stroke: #f59e0b !important;
      stroke-width: 4px !important;
    }

    .highlight-center {
      stroke: #10b981 !important;
      fill: #10b981 !important;
    }

    .callout-badge {
      font-size: 12px;
      font-weight: 700;
      padding: 3px 8px;
      border-radius: 6px;
      color: #ffffff;
      box-shadow: 0 2px 4px rgba(0,0,0,0.15);
      transition: opacity 0.3s ease, transform 0.3s ease;
      pointer-events: none;
    }
  </style>
</head>
<body>

  
  <div class="btn-group">
    <button class="btn active" data-part="all">✦ All Parts</button>
    <button class="btn" data-part="outer"><span class="dot-indicator" style="background:#0284c7;"></span> Outer Scale</button>
    <button class="btn" data-part="inner"><span class="dot-indicator" style="background:#d946ef;"></span> Inner Scale</button>
    <button class="btn" data-part="base"><span class="dot-indicator" style="background:#f59e0b;"></span> Baseline</button>
    <button class="btn" data-part="center"><span class="dot-indicator" style="background:#10b981;"></span> Centre Mark</button>
  </div>

  
  <div class="protractor-container">
    <svg viewBox="0 0 500 270" id="protractorSvg">
      <defs>
        
        <filter id="shadow" x="-5%" y="-5%" width="110%" height="115%">
          <feDropShadow dx="0" dy="4" stdDeviation="6" flood-color="#0f172a" flood-opacity="0.08" />
        </filter>
      </defs>

      
      <path d="M 30,230 A 220,220 0 0,1 470,230 Z" fill="#ffffff" stroke="#cbd5e1" stroke-width="2" filter="url(#shadow)" />
      
      
      <path d="M 160,230 A 90,90 0 0,1 340,230 Z" fill="#f8fafc" stroke="#e2e8f0" stroke-width="1.5" />

      
      <g id="part-base" class="part">
        <line x1="30" y1="230" x2="470" y2="230" stroke="#64748b" stroke-width="2" stroke-linecap="round" />
        <line x1="50" y1="230" x2="450" y2="230" stroke="#0f172a" stroke-width="2" id="baseline-core" />
      </g>

      
      <path id="outer-arc" class="part" d="M 50,230 A 200,200 0 0,1 450,230" fill="none" stroke="#94a3b8" stroke-width="1.5" />
      <path id="inner-arc" class="part" d="M 90,230 A 160,160 0 0,1 410,230" fill="none" stroke="#94a3b8" stroke-width="1.5" />
      <path d="M 125,230 A 125,125 0 0,1 375,230" fill="none" stroke="#e2e8f0" stroke-width="1" />

      
      <g id="ticks-container"></g>
      <g id="part-outer" class="part"></g>
      <g id="part-inner" class="part"></g>

      
      <g id="part-center" class="part">
        
        <circle id="center-ring" cx="250" cy="230" r="16" fill="none" stroke="#64748b" stroke-width="1.5" stroke-dasharray="3,3" />
        <line id="center-v" x1="250" y1="210" x2="250" y2="230" stroke="#0f172a" stroke-width="2" stroke-linecap="round" />
        <line id="center-h" x1="235" y1="230" x2="265" y2="230" stroke="#0f172a" stroke-width="2" stroke-linecap="round" />
        <circle id="center-dot" cx="250" cy="230" r="3.5" fill="#0f172a" />
      </g>

      
      <g id="scale-arrows" class="part" style="transition: opacity 0.3s ease;">
        
        <path d="M 50,218 A 205,205 0 0,1 110,95" fill="none" stroke="#0284c7" stroke-width="2.5" stroke-linecap="round" stroke-dasharray="4,4" id="arrow-outer-path"/>
        <polygon points="112,90 102,96 114,103" fill="#0284c7" id="arrow-outer-head" />
        
        
        <path d="M 450,218 A 205,205 0 0,0 390,95" fill="none" stroke="#d946ef" stroke-width="2.5" stroke-linecap="round" stroke-dasharray="4,4" id="arrow-inner-path"/>
        <polygon points="388,90 386,103 398,96" fill="#d946ef" id="arrow-inner-head" />
      </g>
    </svg>
  </div>

  <script>
    const CX = 250;
    const CY = 230;
    const R_OUTER_TICK = 200;
    const R_INNER_TICK = 160;

    const ticksContainer = document.getElementById('ticks-container');
    const outerGroup = document.getElementById('part-outer');
    const innerGroup = document.getElementById('part-inner');

    // Generate Protractor Ticks and Scale Numbers dynamically
    for (let deg = 0; deg <= 180; deg++) {
      const rad = (180 - deg) * (Math.PI / 180);
      const cos = Math.cos(rad);
      const sin = Math.sin(rad);

      const is10 = deg % 10 === 0;
      const is5 = deg % 5 === 0;

      // Outer Ticks
      const tickLen = is10 ? 12 : (is5 ? 8 : 4);
      const x1 = CX + R_OUTER_TICK * cos;
      const y1 = CY - R_OUTER_TICK * sin;
      const x2 = CX + (R_OUTER_TICK - tickLen) * cos;
      const y2 = CY - (R_OUTER_TICK - tickLen) * sin;

      const tick = document.createElementNS('http://www.w3.org/2000/svg', 'line');
      tick.setAttribute('x1', x1);
      tick.setAttribute('y1', y1);
      tick.setAttribute('x2', x2);
      tick.setAttribute('y2', y2);
      tick.setAttribute('stroke', is10 ? '#334155' : '#94a3b8');
      tick.setAttribute('stroke-width', is10 ? '1.5' : '1');
      ticksContainer.appendChild(tick);

      // Numbers on 10-degree intervals
      if (is10) {
        // Outer scale number: 0 at left (180 deg math), 180 at right (0 deg math)
        // Standard protractor: Outer scale starts 0 on left (180° math pos) to 180 on right
        const rOuterNum = 176;
        const ox = CX + rOuterNum * cos;
        const oy = CY - rOuterNum * sin;

        const outerVal = deg; // 0 to 180 from left to right
        const textOut = document.createElementNS('http://www.w3.org/2000/svg', 'text');
        textOut.setAttribute('x', ox);
        textOut.setAttribute('y', oy);
        textOut.setAttribute('text-anchor', 'middle');
        textOut.setAttribute('dominant-baseline', 'central');
        textOut.setAttribute('font-size', '10');
        textOut.setAttribute('font-weight', '600');
        textOut.setAttribute('fill', '#0284c7');
        textOut.textContent = outerVal;
        outerGroup.appendChild(textOut);

        // Inner scale number: 180 at left, 0 at right
        const rInnerNum = 142;
        const ix = CX + rInnerNum * cos;
        const iy = CY - rInnerNum * sin;

        const innerVal = 180 - deg;
        const textIn = document.createElementNS('http://www.w3.org/2000/svg', 'text');
        textIn.setAttribute('x', ix);
        textIn.setAttribute('y', iy);
        textIn.setAttribute('text-anchor', 'middle');
        textIn.setAttribute('dominant-baseline', 'central');
        textIn.setAttribute('font-size', '10');
        textIn.setAttribute('font-weight', '600');
        textIn.setAttribute('fill', '#d946ef');
        textIn.textContent = innerVal;
        innerGroup.appendChild(textIn);
      }
    }

    // State management for interactive buttons
    const buttons = document.querySelectorAll('.btn');
    const partOuter = document.getElementById('part-outer');
    const partInner = document.getElementById('part-inner');
    const partBase = document.getElementById('part-base');
    const partCenter = document.getElementById('part-center');
    const ticks = document.getElementById('ticks-container');
    const scaleArrows = document.getElementById('scale-arrows');
    const outerArc = document.getElementById('outer-arc');
    const innerArc = document.getElementById('inner-arc');
    const baselineCore = document.getElementById('baseline-core');
    const centerRing = document.getElementById('center-ring');
    const centerDot = document.getElementById('center-dot');
    const centerV = document.getElementById('center-v');
    const centerH = document.getElementById('center-h');
    const arrowOuterPath = document.getElementById('arrow-outer-path');
    const arrowOuterHead = document.getElementById('arrow-outer-head');
    const arrowInnerPath = document.getElementById('arrow-inner-path');
    const arrowInnerHead = document.getElementById('arrow-inner-head');

    function showPart(partName) {
      // Reset all custom styling
      [partOuter, partInner, partBase, partCenter, ticks, scaleArrows, outerArc, innerArc].forEach(el => {
        el.classList.remove('dimmed');
      });

      baselineCore.setAttribute('stroke', '#0f172a');
      baselineCore.setAttribute('stroke-width', '2');
      centerDot.setAttribute('fill', '#0f172a');
      centerRing.setAttribute('stroke', '#64748b');
      centerRing.setAttribute('stroke-width', '1.5');
      centerV.setAttribute('stroke', '#0f172a');
      centerH.setAttribute('stroke', '#0f172a');

      arrowOuterPath.style.display = 'block';
      arrowOuterHead.style.display = 'block';
      arrowInnerPath.style.display = 'block';
      arrowInnerHead.style.display = 'block';

      if (partName === 'outer') {
        partInner.classList.add('dimmed');
        partBase.classList.add('dimmed');
        partCenter.classList.add('dimmed');
        innerArc.classList.add('dimmed');
        arrowInnerPath.style.display = 'none';
        arrowInnerHead.style.display = 'none';
      } else if (partName === 'inner') {
        partOuter.classList.add('dimmed');
        partBase.classList.add('dimmed');
        partCenter.classList.add('dimmed');
        outerArc.classList.add('dimmed');
        arrowOuterPath.style.display = 'none';
        arrowOuterHead.style.display = 'none';
      } else if (partName === 'base') {
        partOuter.classList.add('dimmed');
        partInner.classList.add('dimmed');
        partCenter.classList.add('dimmed');
        ticks.classList.add('dimmed');
        scaleArrows.classList.add('dimmed');
        outerArc.classList.add('dimmed');
        innerArc.classList.add('dimmed');
        baselineCore.setAttribute('stroke', '#f59e0b');
        baselineCore.setAttribute('stroke-width', '4');
      } else if (partName === 'center') {
        partOuter.classList.add('dimmed');
        partInner.classList.add('dimmed');
        partBase.classList.add('dimmed');
        ticks.classList.add('dimmed');
        scaleArrows.classList.add('dimmed');
        outerArc.classList.add('dimmed');
        innerArc.classList.add('dimmed');
        centerDot.setAttribute('fill', '#10b981');
        centerRing.setAttribute('stroke', '#10b981');
        centerRing.setAttribute('stroke-width', '2.5');
        centerV.setAttribute('stroke', '#10b981');
        centerH.setAttribute('stroke', '#10b981');
      }
    }

    buttons.forEach(btn => {
      btn.addEventListener('click', () => {
        buttons.forEach(b => b.classList.remove('active'));
        btn.classList.add('active');
        showPart(btn.dataset.part);
      });
    });
  </script>
</body>
</html>

Where do you place the pointy corner of your shape on this tool?

The little hole or crossmark right in the middle of the flat edge is the **origin**.

The straight flat line running straight across the bottom from zero to zero is the **baseline**.

<!DOCTYPE html>
<html lang="en">
<head>
<meta charset="UTF-8">
<meta name="viewport" content="width=device-width, initial-scale=1.0">
<meta name="aspect-ratio" content="4:3">
<style>
  * { box-sizing: border-box; margin: 0; padding: 0; }
  body {
    font-family: system-ui, -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, sans-serif;
    background: #f8f9fa;
    color: #1e2945;
    display: flex;
    flex-direction: column;
    align-items: center;
    justify-content: space-between;
    min-height: 100%;
    padding: 12px;
    user-select: none;
    -webkit-user-select: none;
  }

  .nav-tabs {
    display: flex;
    flex-wrap: wrap;
    gap: 6px;
    justify-content: center;
    width: 100%;
    max-width: 480px;
    margin-bottom: 8px;
  }

  .tab-btn {
    appearance: none;
    border: 1px solid #e2e8f0;
    background: #ffffff;
    color: #64748b;
    padding: 6px 12px;
    font-size: 13px;
    font-weight: 600;
    border-radius: 20px;
    cursor: pointer;
    transition: all 0.25s ease;
    box-shadow: 0 1px 2px rgba(0,0,0,0.04);
  }

  .tab-btn.active {
    background: #00b4d8;
    color: #ffffff;
    border-color: #00b4d8;
    box-shadow: 0 2px 8px rgba(0, 180, 216, 0.35);
  }

  .svg-container {
    width: 100%;
    max-width: 460px;
    aspect-ratio: 400 / 225;
    position: relative;
    display: flex;
    align-items: center;
    justify-content: center;
  }

  svg {
    width: 100%;
    height: 100%;
    overflow: visible;
  }

  .hl-baseline {
    stroke: #ff4d6d;
    stroke-width: 5;
    stroke-linecap: round;
    opacity: 0;
    transition: opacity 0.3s ease;
  }

  .hl-center {
    fill: #ff4d6d;
    stroke: #ffffff;
    stroke-width: 2;
    opacity: 0;
    transition: opacity 0.3s ease;
  }

  .hl-center-pulse {
    fill: none;
    stroke: #ff4d6d;
    stroke-width: 2;
    opacity: 0;
    transition: opacity 0.3s ease;
  }

  .hl-outer-arc {
    fill: none;
    stroke: #00b4d8;
    stroke-width: 8;
    stroke-linecap: round;
    opacity: 0;
    transition: opacity 0.3s ease;
  }

  .hl-inner-arc {
    fill: none;
    stroke: #ff4d6d;
    stroke-width: 8;
    stroke-linecap: round;
    opacity: 0;
    transition: opacity 0.3s ease;
  }

  .scale-num-outer.active-text {
    fill: #0077b6;
    font-weight: 800;
  }

  .scale-num-inner.active-text {
    fill: #d90429;
    font-weight: 800;
  }

  .indicator-badge {
    margin-top: 4px;
    font-size: 14px;
    font-weight: 700;
    color: #1e2945;
    background: #ffffff;
    padding: 6px 14px;
    border-radius: 12px;
    box-shadow: 0 2px 6px rgba(0,0,0,0.06);
    border: 1px solid #e2e8f0;
    text-align: center;
    min-height: 32px;
    display: flex;
    align-items: center;
    justify-content: center;
  }
</style>
</head>
<body>

<div class="nav-tabs">
  <button class="tab-btn active" data-part="0">Baseline</button>
  <button class="tab-btn" data-part="1">Center Mark</button>
  <button class="tab-btn" data-part="2">Outer Scale</button>
  <button class="tab-btn" data-part="3">Inner Scale</button>
</div>

<div class="svg-container">
  <svg viewBox="0 0 400 220" id="protractorSvg">
    <defs>
      <filter id="glow" x="-20%" y="-20%" width="140%" height="140%">
        <feDropShadow dx="0" dy="1" stdDeviation="2" flood-opacity="0.2"/>
      </filter>
    </defs>

    
    <path d="M 30,190 A 170,170 0 0,1 370,190 Z" fill="#ffffff" stroke="#cbd5e1" stroke-width="2" filter="url(#glow)"/>
    <path d="M 120,190 A 80,80 0 0,1 280,190 Z" fill="#f8fafc" stroke="#e2e8f0" stroke-width="1.5"/>

    
    <g id="ticksGroup"></g>
    <g id="numbersGroup"></g>

    
    <path id="hlOuterArc" class="hl-outer-arc" d="M 40,190 A 160,160 0 0,1 360,190" />
    <path id="hlInnerArc" class="hl-inner-arc" d="M 75,190 A 125,125 0 0,1 325,190" />
    <line id="hlBaseline" class="hl-baseline" x1="30" y1="190" x2="370" y2="190" />
    <line x1="30" y1="190" x2="370" y2="190" stroke="#94a3b8" stroke-width="1.5" />

    
    <circle cx="200" cy="190" r="3" fill="#64748b" />
    <line x1="200" y1="180" x2="200" y2="190" stroke="#64748b" stroke-width="1.5" />
    <circle id="hlCenterPulse" class="hl-center-pulse" cx="200" cy="190" r="10" />
    <circle id="hlCenter" class="hl-center" cx="200" cy="190" r="5" />
  </svg>
</div>

<div class="indicator-badge" id="indicatorBadge">
  Baseline: 0° — 180° Line
</div>

<script>
  const cx = 200;
  const cy = 190;
  const rOuter = 168;
  const ticksGroup = document.getElementById('ticksGroup');
  const numbersGroup = document.getElementById('numbersGroup');

  // Build accurate degree ticks & numbers
  for (let deg = 0; deg <= 180; deg += 5) {
    const rad = (deg * Math.PI) / 180;
    const cos = Math.cos(rad);
    const sin = Math.sin(rad);

    const isMajor = deg % 10 === 0;
    const is30 = deg % 30 === 0;
    const tickLen = is30 ? 10 : (isMajor ? 7 : 4);

    const x1 = cx - (rOuter - tickLen) * cos;
    const y1 = cy - (rOuter - tickLen) * sin;
    const x2 = cx - rOuter * cos;
    const y2 = cy - rOuter * sin;

    const line = document.createElementNS('http://www.w3.org/2000/svg', 'line');
    line.setAttribute('x1', x1);
    line.setAttribute('y1', y1);
    line.setAttribute('x2', x2);
    line.setAttribute('y2', y2);
    line.setAttribute('stroke', isMajor ? '#64748b' : '#94a3b8');
    line.setAttribute('stroke-width', isMajor ? '1.5' : '1');
    ticksGroup.appendChild(line);

    if (is30) {
      // Outer Scale numbers (0 to 180, right to left)
      const rTextOut = 146;
      const txOut = cx - rTextOut * cos;
      const tyOut = cy - rTextOut * sin + 4;

      const textOut = document.createElementNS('http://www.w3.org/2000/svg', 'text');
      textOut.setAttribute('x', txOut);
      textOut.setAttribute('y', tyOut);
      textOut.setAttribute('text-anchor', 'middle');
      textOut.setAttribute('font-size', '10');
      textOut.setAttribute('fill', '#475569');
      textOut.setAttribute('class', 'scale-num-outer');
      textOut.setAttribute('data-deg', 180 - deg);
      textOut.textContent = (180 - deg);
      numbersGroup.appendChild(textOut);

      // Inner Scale numbers (0 to 180, left to right)
      const rTextIn = 104;
      const txIn = cx - rTextIn * cos;
      const tyIn = cy - rTextIn * sin + 4;

      const textIn = document.createElementNS('http://www.w3.org/2000/svg', 'text');
      textIn.setAttribute('x', txIn);
      textIn.setAttribute('y', tyIn);
      textIn.setAttribute('text-anchor', 'middle');
      textIn.setAttribute('font-size', '9');
      textIn.setAttribute('fill', '#64748b');
      textIn.setAttribute('class', 'scale-num-inner');
      textIn.setAttribute('data-deg', deg);
      textIn.textContent = deg;
      numbersGroup.appendChild(textIn);
    }
  }

  const parts = [
    {
      label: 'Baseline: 0° — 180° Line',
      show: () => {
        document.getElementById('hlBaseline').style.opacity = '1';
      }
    },
    {
      label: 'Center Mark: Vertex Alignment',
      show: () => {
        document.getElementById('hlCenter').style.opacity = '1';
        document.getElementById('hlCenterPulse').style.opacity = '1';
      }
    },
    {
      label: 'Outer Scale: 0° (Right) → 180°',
      show: () => {
        document.getElementById('hlOuterArc').style.opacity = '0.4';
        document.querySelectorAll('.scale-num-outer').forEach(el => el.classList.add('active-text'));
      }
    },
    {
      label: 'Inner Scale: 0° (Left) → 180°',
      show: () => {
        document.getElementById('hlInnerArc').style.opacity = '0.4';
        document.querySelectorAll('.scale-num-inner').forEach(el => el.classList.add('active-text'));
      }
    }
  ];

  function resetHighlights() {
    document.getElementById('hlBaseline').style.opacity = '0';
    document.getElementById('hlCenter').style.opacity = '0';
    document.getElementById('hlCenterPulse').style.opacity = '0';
    document.getElementById('hlOuterArc').style.opacity = '0';
    document.getElementById('hlInnerArc').style.opacity = '0';
    document.querySelectorAll('.scale-num-outer').forEach(el => el.classList.remove('active-text'));
    document.querySelectorAll('.scale-num-inner').forEach(el => el.classList.remove('active-text'));
  }

  const tabs = document.querySelectorAll('.tab-btn');
  const badge = document.getElementById('indicatorBadge');

  function setPart(index) {
    tabs.forEach((tab, i) => {
      tab.classList.toggle('active', i === index);
    });
    resetHighlights();
    parts[index].show();
    badge.textContent = parts[index].label;
  }

  tabs.forEach((tab, i) => {
    tab.addEventListener('click', () => setPart(i));
  });

  // Initial State
  setPart(0);
</script>

</body>
</html>

Why are there two curved rows of numbers around the curved edge?

The **outer scale** is the row of numbers on the outside curve that starts at 0 on the left and goes up to 180 on the right.

The **inner scale** is the row of numbers on the inside curve that starts at 0 on the right and goes up to 180 on the left.

<!DOCTYPE html>
<html lang="en">
<head>
  <meta charset="UTF-8">
  <meta name="viewport" content="width=device-width, initial-scale=1.0">
  <meta name="aspect-ratio" content="4:3">
  <title>180-Degree Protractor Scales</title>
  <style>
    * {
      box-sizing: border-box;
      margin: 0;
      padding: 0;
      user-select: none;
      -webkit-user-select: none;
    }
    body {
      font-family: system-ui, -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, sans-serif;
      background-color: #f8f9fa;
      color: #1e2945;
      display: flex;
      flex-direction: column;
      align-items: center;
      justify-content: space-between;
      min-height: 100%;
      padding: 10px;
      overflow-x: hidden;
    }
    .controls {
      display: flex;
      flex-wrap: wrap;
      gap: 6px;
      justify-content: center;
      width: 100%;
      max-width: 520px;
      margin-bottom: 6px;
    }
    .btn {
      background: #ffffff;
      border: 1.5px solid #e2e8f0;
      color: #64748b;
      font-size: 13px;
      font-weight: 600;
      padding: 6px 12px;
      border-radius: 20px;
      cursor: pointer;
      display: inline-flex;
      align-items: center;
      gap: 6px;
      transition: all 0.2s ease;
    }
    .btn.active-inner {
      background: #7209b7;
      color: #ffffff;
      border-color: #7209b7;
      box-shadow: 0 2px 8px rgba(114, 9, 183, 0.3);
    }
    .btn.active-outer {
      background: #f77f00;
      color: #ffffff;
      border-color: #f77f00;
      box-shadow: 0 2px 8px rgba(247, 127, 0, 0.3);
    }
    .btn.active-parts {
      background: #0ea5e9;
      color: #ffffff;
      border-color: #0ea5e9;
      box-shadow: 0 2px 8px rgba(14, 165, 233, 0.3);
    }
    .btn.active-measure {
      background: #10b981;
      color: #ffffff;
      border-color: #10b981;
      box-shadow: 0 2px 8px rgba(16, 185, 129, 0.3);
    }
    .diagram-area {
      width: 100%;
      max-width: 520px;
      position: relative;
      display: flex;
      justify-content: center;
      align-items: center;
    }
    svg {
      width: 100%;
      height: auto;
      display: block;
      touch-action: none;
    }
    .scale-text {
      font-size: 11px;
      font-weight: 700;
      font-family: system-ui, sans-serif;
      text-anchor: middle;
      dominant-baseline: central;
      transition: fill 0.25s ease, opacity 0.25s ease;
    }
    .outer-num { fill: #f77f00; }
    .inner-num { fill: #7209b7; }
    .dimmed { opacity: 0.18; }
    .highlight-scale { opacity: 1; font-weight: 900; }
    
    .interactive-slider-box {
      width: 100%;
      max-width: 440px;
      display: flex;
      flex-direction: column;
      align-items: center;
      gap: 4px;
      margin-top: 4px;
    }
    .slider-row {
      display: flex;
      align-items: center;
      width: 100%;
      gap: 10px;
    }
    input[type="range"] {
      flex: 1;
      accent-color: #10b981;
      cursor: pointer;
      height: 6px;
    }
    .readout-badge {
      display: flex;
      gap: 8px;
      font-size: 13px;
      font-weight: 700;
    }
    .badge-inner {
      color: #7209b7;
      background: rgba(114, 9, 183, 0.1);
      padding: 3px 8px;
      border-radius: 6px;
    }
    .badge-outer {
      color: #f77f00;
      background: rgba(247, 127, 0, 0.12);
      padding: 3px 8px;
      border-radius: 6px;
    }
    .dir-indicator {
      font-size: 12px;
      font-weight: 700;
      transition: opacity 0.25s ease;
    }
  </style>
</head>
<body>

  <div class="controls">
    <button class="btn active-inner" id="btnInner">Inner Scale (0° Right ➔)</button>
    <button class="btn" id="btnOuter">Outer Scale (0° Left ➔)</button>
    <button class="btn" id="btnParts">Center & Base</button>
    <button class="btn" id="btnMeasure">Angle Ray</button>
  </div>

  <div class="diagram-area">
    <svg viewBox="0 0 500 280" id="protractorSvg">
      <defs>
        
        <marker id="arrow-purple" viewBox="0 0 10 10" refX="6" refY="5" markerWidth="6" markerHeight="6" orient="auto-start-reverse">
          <path d="M 0 1 L 10 5 L 0 9 z" fill="#7209b7" />
        </marker>
        <marker id="arrow-orange" viewBox="0 0 10 10" refX="6" refY="5" markerWidth="6" markerHeight="6" orient="auto-start-reverse">
          <path d="M 0 1 L 10 5 L 0 9 z" fill="#f77f00" />
        </marker>
      </defs>

      
      <path d="M 30,230 A 220,220 0 0,1 470,230 Z" fill="#ffffff" stroke="#cbd5e1" stroke-width="2.5" />
      <path d="M 180,230 A 70,70 0 0,1 320,230 Z" fill="#f8fafc" stroke="#e2e8f0" stroke-width="1.5" />

      
      
      <path id="innerFlow" d="M 385,225 A 135,135 0 0,0 115,225" fill="none" stroke="#7209b7" stroke-width="3" stroke-dasharray="4,4" marker-end="url(#arrow-purple)" opacity="1" />
      
      
      <path id="outerFlow" d="M 55,215 A 195,195 0 0,1 445,215" fill="none" stroke="#f77f00" stroke-width="3" stroke-dasharray="4,4" marker-end="url(#arrow-orange)" opacity="0" />

      
      <g id="ticksGroup"></g>

      
      <path id="angleWedge" d="" fill="rgba(16, 185, 129, 0.15)" stroke="none" opacity="0"></path>
      <line id="angleRay" x1="250" y1="230" x2="391" y2="89" stroke="#10b981" stroke-width="3.5" stroke-linecap="round" opacity="0" />
      <circle id="rayHandle" cx="391" cy="89" r="7" fill="#10b981" stroke="#ffffff" stroke-width="2" opacity="0" />

      
      <line id="baseLine" x1="30" y1="230" x2="470" y2="230" stroke="#0ea5e9" stroke-width="3.5" opacity="0" />
      
      
      <g id="centerMark">
        <line x1="250" y1="218" x2="250" y2="230" stroke="#64748b" stroke-width="1.5" />
        <circle id="centerDot" cx="250" cy="230" r="5" fill="#0ea5e9" stroke="#ffffff" stroke-width="1.5" />
      </g>

      
      <g id="partsLabels" opacity="0">
        
        <rect x="185" y="246" width="130" height="24" rx="12" fill="#0ea5e9" />
        <text x="250" y="258" fill="#ffffff" font-size="12" font-weight="700" text-anchor="middle" dominant-baseline="central">Baseline (0° Line)</text>
        <line x1="250" y1="246" x2="250" y2="234" stroke="#0ea5e9" stroke-width="2" />

        
        <rect x="195" y="150" width="110" height="22" rx="11" fill="#0ea5e9" />
        <text x="250" y="161" fill="#ffffff" font-size="12" font-weight="700" text-anchor="middle" dominant-baseline="central">Center Origin</text>
        <line x1="250" y1="172" x2="250" y2="222" stroke="#0ea5e9" stroke-width="1.5" stroke-dasharray="2,2" />
      </g>

      
      <g id="zeroPrompts">
        <text id="zeroRightTag" x="430" y="244" fill="#7209b7" font-size="11" font-weight="800" text-anchor="middle">0° START</text>
        <text id="zeroLeftTag" x="70" y="244" fill="#f77f00" font-size="11" font-weight="800" text-anchor="middle" opacity="0.2">0° START</text>
      </g>
    </svg>
  </div>

  
  <div class="interactive-slider-box" id="sliderBox">
    <div class="slider-row">
      <span style="font-size:12px;font-weight:700;color:#64748b;">0°</span>
      <input type="range" id="angleSlider" min="0" max="180" value="45">
      <span style="font-size:12px;font-weight:700;color:#64748b;">180°</span>
    </div>
    <div class="readout-badge">
      <span class="badge-inner" id="innerBadge">Inner Scale: 45°</span>
      <span class="badge-outer" id="outerBadge">Outer Scale: 135°</span>
    </div>
  </div>

  <script>
    const cx = 250;
    const cy = 230;
    const rOuterEdge = 220;
    const rOuterText = 196;
    const rInnerText = 158;
    const rInnerArc = 142;

    const ticksGroup = document.getElementById('ticksGroup');
    const btnInner = document.getElementById('btnInner');
    const btnOuter = document.getElementById('btnOuter');
    const btnParts = document.getElementById('btnParts');
    const btnMeasure = document.getElementById('btnMeasure');

    const innerFlow = document.getElementById('innerFlow');
    const outerFlow = document.getElementById('outerFlow');
    const baseLine = document.getElementById('baseLine');
    const partsLabels = document.getElementById('partsLabels');
    const centerDot = document.getElementById('centerDot');
    const zeroRightTag = document.getElementById('zeroRightTag');
    const zeroLeftTag = document.getElementById('zeroLeftTag');

    const angleRay = document.getElementById('angleRay');
    const rayHandle = document.getElementById('rayHandle');
    const angleWedge = document.getElementById('angleWedge');
    const angleSlider = document.getElementById('angleSlider');
    const innerBadge = document.getElementById('innerBadge');
    const outerBadge = document.getElementById('outerBadge');

    let currentMode = 'inner';

    // Generate accurate tick lines and scale numbers
    for (let deg = 0; deg <= 180; deg += 1) {
      const rad = (180 - deg) * Math.PI / 180;
      const cos = Math.cos(rad);
      const sin = Math.sin(rad);

      let tickLen = 0;
      let strokeWidth = 1;
      let strokeColor = '#94a3b8';

      if (deg % 10 === 0) {
        tickLen = 14;
        strokeWidth = 1.5;
        strokeColor = '#475569';
      } else if (deg % 5 === 0) {
        tickLen = 9;
        strokeWidth = 1;
        strokeColor = '#64748b';
      } else {
        tickLen = 5;
        strokeWidth = 0.6;
        strokeColor = '#cbd5e1';
      }

      const x1 = cx + rOuterEdge * cos;
      const y1 = cy - rOuterEdge * sin;
      const x2 = cx + (rOuterEdge - tickLen) * cos;
      const y2 = cy - (rOuterEdge - tickLen) * sin;

      const line = document.createElementNS('http://www.w3.org/2000/svg', 'line');
      line.setAttribute('x1', x1);
      line.setAttribute('y1', y1);
      line.setAttribute('x2', x2);
      line.setAttribute('y2', y2);
      line.setAttribute('stroke', strokeColor);
      line.setAttribute('stroke-width', strokeWidth);
      ticksGroup.appendChild(line);

      // Inner divider ticks at inner radius
      if (deg % 10 === 0) {
        const ix1 = cx + rInnerArc * cos;
        const iy1 = cy - rInnerArc * sin;
        const ix2 = cx + (rInnerArc + 7) * cos;
        const iy2 = cy - (rInnerArc + 7) * sin;
        const iline = document.createElementNS('http://www.w3.org/2000/svg', 'line');
        iline.setAttribute('x1', ix1);
        iline.setAttribute('y1', iy1);
        iline.setAttribute('x2', ix2);
        iline.setAttribute('y2', iy2);
        iline.setAttribute('stroke', '#cbd5e1');
        iline.setAttribute('stroke-width', '1');
        ticksGroup.appendChild(iline);
      }

      // Add Numbers every 10 degrees
      if (deg % 10 === 0) {
        const outerVal = deg; // 0 on left (180 math angle), 180 on right
        const innerVal = 180 - deg; // 0 on right, 180 on left

        // Outer Number
        const ox = cx + rOuterText * cos;
        const oy = cy - rOuterText * sin;
        const ot = document.createElementNS('http://www.w3.org/2000/svg', 'text');
        ot.setAttribute('x', ox);
        ot.setAttribute('y', oy);
        ot.setAttribute('class', 'scale-text outer-num');
        ot.setAttribute('data-val', outerVal);
        ot.textContent = outerVal;
        ticksGroup.appendChild(ot);

        // Inner Number
        const ix = cx + rInnerText * cos;
        const iy = cy - rInnerText * sin;
        const it = document.createElementNS('http://www.w3.org/2000/svg', 'text');
        it.setAttribute('x', ix);
        it.setAttribute('y', iy);
        it.setAttribute('class', 'scale-text inner-num');
        it.setAttribute('data-val', innerVal);
        it.textContent = innerVal;
        ticksGroup.appendChild(it);
      }
    }

    // Mode Switching
    function setMode(mode) {
      currentMode = mode;
      btnInner.className = 'btn' + (mode === 'inner' ? ' active-inner' : '');
      btnOuter.className = 'btn' + (mode === 'outer' ? ' active-outer' : '');
      btnParts.className = 'btn' + (mode === 'parts' ? ' active-parts' : '');
      btnMeasure.className = 'btn' + (mode === 'measure' ? ' active-measure' : '');

      const outerNums = document.querySelectorAll('.outer-num');
      const innerNums = document.querySelectorAll('.inner-num');

      if (mode === 'inner') {
        outerNums.forEach(el => el.classList.add('dimmed'));
        innerNums.forEach(el => el.classList.remove('dimmed'));
        innerFlow.style.opacity = '1';
        outerFlow.style.opacity = '0';
        baseLine.style.opacity = '0';
        partsLabels.style.opacity = '0';
        zeroRightTag.style.opacity = '1';
        zeroLeftTag.style.opacity = '0.2';
        setRayVisible(false);
      } else if (mode === 'outer') {
        outerNums.forEach(el => el.classList.remove('dimmed'));
        innerNums.forEach(el => el.classList.add('dimmed'));
        innerFlow.style.opacity = '0';
        outerFlow.style.opacity = '1';
        baseLine.style.opacity = '0';
        partsLabels.style.opacity = '0';
        zeroRightTag.style.opacity = '0.2';
        zeroLeftTag.style.opacity = '1';
        setRayVisible(false);
      } else if (mode === 'parts') {
        outerNums.forEach(el => el.classList.add('dimmed'));
        innerNums.forEach(el => el.classList.add('dimmed'));
        innerFlow.style.opacity = '0';
        outerFlow.style.opacity = '0';
        baseLine.style.opacity = '1';
        partsLabels.style.opacity = '1';
        zeroRightTag.style.opacity = '0.2';
        zeroLeftTag.style.opacity = '0.2';
        setRayVisible(false);
      } else if (mode === 'measure') {
        outerNums.forEach(el => el.classList.remove('dimmed'));
        innerNums.forEach(el => el.classList.remove('dimmed'));
        innerFlow.style.opacity = '0';
        outerFlow.style.opacity = '0';
        baseLine.style.opacity = '0';
        partsLabels.style.opacity = '0';
        zeroRightTag.style.opacity = '0.5';
        zeroLeftTag.style.opacity = '0.5';
        setRayVisible(true);
        updateRay(angleSlider.value);
      }
    }

    function setRayVisible(show) {
      const op = show ? '1' : '0';
      angleRay.style.opacity = op;
      rayHandle.style.opacity = op;
      angleWedge.style.opacity = show ? '1' : '0';
    }

    function updateRay(degFromRight) {
      const angle = Number(degFromRight);
      const rad = angle * Math.PI / 180;
      const rayR = 210;
      const x = cx + rayR * Math.cos(rad);
      const y = cy - rayR * Math.sin(rad);

      angleRay.setAttribute('x2', x);
      angleRay.setAttribute('y2', y);
      rayHandle.setAttribute('cx', x);
      rayHandle.setAttribute('cy', y);

      // Wedge path from baseline (right)
      const wedgeR = 120;
      const wx = cx + wedgeR * Math.cos(rad);
      const wy = cy - wedgeR * Math.sin(rad);
      const largeArc = angle > 180 ? 1 : 0;
      const wedgePath = `M ${cx} ${cy} L ${cx + wedgeR} ${cy} A ${wedgeR} ${wedgeR} 0 ${largeArc} 0 ${wx} ${wy} Z`;
      angleWedge.setAttribute('d', wedgePath);

      innerBadge.textContent = `Inner: ${angle}° (from Right 0°)`;
      outerBadge.textContent = `Outer: ${180 - angle}° (from Left 0°)`;
    }

    btnInner.addEventListener('click', () => setMode('inner'));
    btnOuter.addEventListener('click', () => setMode('outer'));
    btnParts.addEventListener('click', () => setMode('parts'));
    btnMeasure.addEventListener('click', () => setMode('measure'));

    angleSlider.addEventListener('input', (e) => {
      if (currentMode !== 'measure') setMode('measure');
      updateRay(e.target.value);
    });

    // Touch / Click protractor to move ray
    const svgEl = document.getElementById('protractorSvg');
    function handlePointer(e) {
      if (currentMode !== 'measure') return;
      const rect = svgEl.getBoundingClientRect();
      const clientX = e.touches ? e.touches[0].clientX : e.clientX;
      const clientY = e.touches ? e.touches[0].clientY : e.clientY;
      const svgX = ((clientX - rect.left) / rect.width) * 500;
      const svgY = ((clientY - rect.top) / rect.height) * 280;

      const dx = svgX - cx;
      const dy = cy - svgY;
      let angleRad = Math.atan2(dy, dx);
      if (angleRad < 0) angleRad = 0;
      if (angleRad > Math.PI) angleRad = Math.PI;

      const deg = Math.round(angleRad * 180 / Math.PI);
      angleSlider.value = deg;
      updateRay(deg);
    }

    let isDragging = false;
    svgEl.addEventListener('pointerdown', (e) => {
      if (currentMode === 'measure') {
        isDragging = true;
        handlePointer(e);
      }
    });
    window.addEventListener('pointermove', (e) => {
      if (isDragging) handlePointer(e);
    });
    window.addEventListener('pointerup', () => { isDragging = false; });

    // Initial setup
    setMode('inner');
    updateRay(45);
  </script>
</body>
</html>

A common mistake is reading the top number instead of checking which side starts at zero.

Always look at your bottom line first and pick the scale that starts counting at **0**, not 180!

math

Understanding the Parts and Scales of a 180-Degree Protractor. Identify the origin, baseline, inner scale, and outer scale of a semi-circular protractor.

How to Measure Angles with a Protractor (CfE Second Level MTH 2-17b)

Measuring Angles Using a Protractor

Measure Angles with a 180-Degree Protractor

Under Scotland's Curriculum for Excellence (CfE), standard MTH 2-17b sits within Second Level (typically P5–P7 / ages 9–12), where formal protractor anatomy is systematically taught. When introducing this tool, pedagogical best practice emphasizes tactile discovery using transparent physical protractors to explore the origin and baseline before measuring angles. Teachers should scaffold learning by having students physically trace the zero line and count up from $0^\circ$ rather than reading numbers in isolation.

Understanding the Parts and Scales of a 180-Degree Protractor

The Origin and Baseline

Two Sets of Numbers