supplementary angles

Two angles are called supplementary angles  of each other if the sum of their measures (http://planetmath.org/AngleMeasure) is equal to the straight angle $\pi$, i.e. (http://planetmath.org/Ie) ${180}^{\circ }$.

For example, when two lines intersect each other, they the plane into four disjoint domains (http://planetmath.org/Domain2) 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. (http://planetmath.org/Eg) an entry regarding opposing angles in a cyclic quadrilateral (http://planetmath.org/OpposingAnglesInACyclicQuadrilateralAreSupplementary).

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

$$\sin (\pi -\alpha )=\sin \alpha ,\cos (\pi -\alpha )=-\cos \alpha$$

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

Title	supplementary angles
Canonical name	SupplementaryAngles
Date of creation	2013-03-22 17:34:59
Last modified on	2013-03-22 17:34:59
Owner	pahio (2872)
Last modified by	pahio (2872)
Numerical id	8
Author	pahio (2872)
Entry type	Definition
Classification	msc 51M04
Classification	msc 51F20
Synonym	supplementary
Related topic	Supplement
Related topic	Angle
Related topic	ComplementaryAngles
Related topic	GoniometricFormulae