supplementary angles

Two angles are called supplementary anglesMathworldPlanetmath  of each other if the sum of their measures ( is equal to the straight angleMathworldPlanetmath π, i.e. ( 180.

For example, when two lines intersect each other, they 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 quadrilateralMathworldPlanetmath (

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


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