Complementary angles are two angles whose measures add up to exactly 90 degrees. When two angles sum to 90 degrees, they are called complementary and each is referred to as the complement of the other. These angles can either be adjacent (sharing a common vertex and arm) or non-adjacent. For example, if one angle is 30 degrees, the complementary angle would be 60 degrees because 30° + 60° = 90°. Together, complementary angles form a right angle. In summary:
- Two angles are complementary if their sum is 90 degrees.
- Each angle is the complement of the other.
- They can be adjacent or non-adjacent.
- They form a right angle when combined.
This concept is fundamental in geometry and is often used in trigonometry, where the complementary relationship between angles affects trigonometric ratios like sine and cosine. The word "complementary" comes from Latin meaning "to complete," reflecting that two complementary angles complete a right angle together. If one angle is known, the other can be found by subtracting the known angle from 90 degrees. This definition and explanation come from multiple reliable educational sources.
