Geometry
Complementary Angles – Pairs That Add to 90°
Two angles are complementary if their measures add up to exactly 90° – a right angle. The two angles don't need to be next to each other or drawn in any particular way; the only requirement is that their measures sum to 90°. To find the complement of a known angle, simply subtract it from 90°.
“Complementary” comes from the Latin complementum, meaning “that which completes” – a complementary angle is exactly what's needed to complete the pair into a full right angle.
Finding a Complement
Two angles are complementary if they sum to 90°. To find the complement of angle x, calculate 90° − x.
Find the complement of 37°.
90 − 37 = 53°.
Are 62° and 28° complementary?
62 + 28 = 90°. Since they sum to 90°, yes, they are complementary.
Real-Life Application
- Carpentry joints: some corner joints are designed using complementary angle cuts.
- Ramps and staircases: a ramp's incline and its complement describe the space it occupies.
- Optics: some mirror and lens setups rely on complementary angle relationships.
Key Takeaways
- Complementary angles sum to exactly 90°.
- The complement of angle x is 90° − x.
- The angles don't need to be adjacent to be complementary.
Practice: Complementary Angles
Complementary Angles