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What Are Complementary Angles?
Updated Math & Study Help
Examples of complementary angle pairs
- 30° and 60° (30 + 60 = 90)
- 45° and 45° (two equal angles, 45 + 45 = 90)
- 10° and 80° (10 + 80 = 90)
- 72° and 18° (72 + 18 = 90)
Complementary vs. supplementary — the distinction most people are actually looking for
| Term | Angles add up to | Memory trick |
|---|---|---|
| Complementary | 90° (a right angle) | "C" comes before "S" in the alphabet, and 90 comes before 180 |
| Supplementary | 180° (a straight line) | Think "Straight" line for "Supplementary" |
Finding a missing complementary angle: if one angle is known, subtract it from 90° to find its complement. Example: if one angle is 35°, its complement is 90 − 35 = 55°, since 35° + 55° = 90°.
Do complementary angles have to be next to each other? No. Complementary angles are defined purely by their measures adding to 90° — they don't need to share a vertex or side (that's called being "adjacent," a separate property that many complementary angle pairs happen to have, like the two acute angles inside a right triangle, but it isn't required for the definition).
Real-world example: the two non-right angles inside any right triangle are always complementary, since all three angles in a triangle add up to 180°, and one of them is already 90°, leaving exactly 90° to be split between the other two.
Two similar answers: What Are Supplementary Angles? and What Does Congruent Mean?.
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