Geometry
Supplementary Angles – Pairs That Add to 180°
Two angles are supplementary if their measures add up to exactly 180° – a straight angle. Just like complementary angles, supplementary angles don't need to be next to each other; the only rule is that the two measures sum to 180°. To find the supplement of a known angle, subtract it from 180°.
“Supplementary” comes from the Latin supplere, meaning “to supply” or “to complete” – a supplementary angle supplies exactly what's missing to complete a straight 180° line. A simple way to keep “complementary” and “supplementary” straight: C comes before S alphabetically, and 90 comes before 180 numerically.
Finding a Supplement
Two angles are supplementary if they sum to 180°. To find the supplement of angle x, calculate 180° − x.
180 − 112 = 68°.
95 + 85 = 180°. Since they sum to 180°, yes, they are supplementary.
Real-Life Application
- Adjustable lamps: the hinge angle and its supplement together describe how far a lamp arm can fold.
- Road signs: some warning signs use supplementary angle pairs to show opposite directions.
- Door hinges: a door's open angle and its supplement together span a straight line.
Key Takeaways
- Supplementary angles sum to exactly 180°.
- The supplement of angle x is 180° − x.
- The angles don't need to be adjacent to be supplementary.