Complementary and Supplementary Angles

Geometry · Axiom Academy

LESSON Complementary and Supplementary Angles How two angles pair up to make the two most important sums in geometry: a right angle of 90° and a straight angle of 180°. Two angles are complementary if their measures add up to exactly 90° — a right angle. Watch a single ray swing up from the horizontal: it splits the right angle into two pieces, and no matter where it stops, those two pieces always total 90°. The two parts of a right angle Two angles are supplementary if their measures add up to exactly 180° — a straight angle. Here a ray pivots on a straight line: whatever angle it makes on one side, the angle on the other side is whatever is left over to complete the straight line. Any two angles that sit side-by-side on a straight line are supplementary — together they sweep the full 180°. That side-by-side pair on a line has a name: a linear pair . Linear pairs are always supplementary. The two parts of a straight angle Complementary makes a corner (90°); supplementary makes a flat line (180°). A handy memory hook: C omplementary comes before S upplementary in the alphabet, just as 90 comes before 180. Once you know the sum, finding a missing angle is just subtraction. To find a complement , subtract from 90°; to find a supplement , subtract from 180°. In the animation, a known angle is drawn first and the missing piece fills in the rest of the right angle, then the rest of the straight angle.

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