AI Tutor
Imagine building a skateboard ramp where two wooden beams meet to form a crisp, square corner. If the ground slope is 35∘35^\circ, how do you know the exact cut for the second beam without guessing?
When two angles add up to make a square corner of 90∘90^\circ, they are called complementary angles.
A full circular turn is 360∘360^\circ, so a quarter-turn forms an exact right angle of 90∘90^\circ.
To find an unknown complementary angle xx, subtract the known angle from 90∘90^\circ: x=90∘−35∘=55∘x = 90^\circ - 35^\circ = 55^\circ.
What happens when an unknown angle is written with an algebraic expression instead of a single number?

Algebraic Complementary Angles

When angle expressions share a right corner, write an equation setting their sum equal to 90∘90^\circ.
Combine like terms to get 2x+40=902x + 40 = 90, subtract 4040 from both sides to get 2x=502x = 50, and divide by 22 to find x=25x = 25.
What if the angles sit side-by-side along a flat, straight line instead of a right corner?

Supplementary Angles and Straight Lines

Two angles that combine to form a flat line are called supplementary angles, and their measures always add up to 180∘180^\circ.