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Look at the corner of a book, a sheet of paper, or a door frame. They all meet at a perfect square corner called a right angle, which measures exactly 90∘90^\circ.
In global curricula like China Compulsory, UK KS3, and Australia ACARA, Rigorous Deduction forbids assuming an angle is 90∘90^\circ purely from visual appearance.
It must be marked with explicit Geometric Notation: either a right-angle square symbol (⌞\llcorner) at the vertex or by stating that two lines are perpendicular (AB⊥CDAB \perp CD).
What happens when you draw a ray through that square corner to split it into two smaller pieces?

Splitting a Right Angle

When two angles add up to 90∘90^\circ, we call them complementary angles. Each angle is called the complement of the other.
Partitioning a right angle by one or more interior rays from the vertex is called a Right Angle Decomposition.
Under the Angle Addition Postulate, the adjacent parts equal the whole: ∠1+∠2=90∘\angle 1 + \angle 2 = 90^\circ, or ∑i=1n∠i=90∘\sum_{i=1}^n \angle i = 90^\circ for multi-split decompositions.
The name comes from the Latin word complementum, meaning "that which completes" — because together, they complete a full 90∘90^\circ corner.
Complementary angles can be Adjacent Complementary Pairs that share a vertex and ray, or non-adjacent angles separated across the plane.
For example, the two acute angles in any right-angled triangle form a non-adjacent pair because ∠A+∠B=90∘\angle A + \angle B = 90^\circ.