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# supplementary angles

Two angles are called supplementary angles of each other if the sum of their measures is equal to the straight angle $\pi$, i.e. $180^{\circ}$.

For example, when two lines intersect each other, they divide the plane into four disjoint domains corresponding to four convex angles; then any of these angles has a supplementary angle on either side of it (see linear pair). However, two angles that are supplementary to each other do not need to have a common side — see e.g. an entry regarding opposing angles in a cyclic quadrilateral.

Supplementary angles have always equal sines, but the cosines are opposite numbers:

$\sin(\pi\!-\!\alpha)\;=\;\sin\alpha,\qquad\cos(\pi\!-\!\alpha)\;=\;-\cos\alpha$ |

These formulae may be proved by using the subtraction formulas of sine and cosine.

Related:

Supplement, Angle, ComplementaryAngles, GoniometricFormulae

Synonym:

supplementary

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Definition

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## Mathematics Subject Classification

51M04*no label found*51F20

*no label found*

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