# Complementary angles

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Complementary angles
A pair of complementary angles, because their measures add up to 90 degrees

In geometry, complementary angles are angles whose measures sum to 90°. If the two complementary angles are adjacent (i.e. have a common vertex and share just one side) their non-shared sides form a right angle.

In Euclidean geometry, the two acute angles in a right triangle are complementary, because the sum of internal angles of a triangle is 180 degrees, and the right angle itself accounts for ninety degrees.

The adjective complementary is from Latin complementum, associated with the verb complere, "to fill up". An acute angle is "filled up" by its complement to form a right angle.

## Trigonometric ratios

The sine of an angle equals the cosine of its complementary angle. It is therefore true that, if angles A and B are complementary, sin2A + sin2B = 1, and cos2A + cos2B = 1.

The tangent of an angle equals the cotangent of its complementary angle. The tangents of complementary angles are reciprocals of each other.

The secant of an angle equals the cosecant of its complementary angle.

The prefix "co-" in the names of some trigonometric ratios refers to the word "complementary".

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### Look at other dictionaries:

• Complementary angles — Complementary Com ple*men ta*ry, a. Serving to fill out or to complete; as, complementary numbers. [1913 Webster] {Complementary colors}. See under {Color}. {Complementary angles} (Math.), two angles whose sum is 90[deg]. [1913 Webster] …   The Collaborative International Dictionary of English

• complementary angles — noun two angles whose sum is a right angle • Hypernyms: ↑angle * * * noun plural : two angles whose sum is a right angle * * * complementary angles UK US noun [plural] maths two angles that together form a right angle …   Useful english dictionary

• complementary angles — noun A pair of angles that sum to a right angle …   Wiktionary

• complementary angles — n. angles whose sum equals to 90 degrees …   English contemporary dictionary

• complementary angles — UK / US noun [plural] maths two angles that together form a right angle …   English dictionary

• Complementary — Com ple*men ta*ry, a. Serving to fill out or to complete; as, complementary numbers. [1913 Webster] {Complementary colors}. See under {Color}. {Complementary angles} (Math.), two angles whose sum is 90[deg]. [1913 Webster] …   The Collaborative International Dictionary of English

• Complementary colors — Complementary Com ple*men ta*ry, a. Serving to fill out or to complete; as, complementary numbers. [1913 Webster] {Complementary colors}. See under {Color}. {Complementary angles} (Math.), two angles whose sum is 90[deg]. [1913 Webster] …   The Collaborative International Dictionary of English

• complementary angle — ► NOUN ▪ either of two angles whose sum is 90° …   English terms dictionary

• complementary angle — n. either of two angles that together form a 90° angle …   English World dictionary

• complementary angle — Math. either of two angles that added together produce an angle of 90°. Cf. supplementary angle. * * * ˌcomplementary ˈangle [complementary angle] noun (geometry) either of two angles which together make 90° …   Useful english dictionary