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.