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Supplementary Angles


SupplementaryAngles

Supplementary angles are two angles alpha and beta whose measures satisfy alpha+beta=180 degrees, the measure of a straight angle. Equivalently, their measures sum to pi radians.

When measured in degrees, the supplement of an angle alpha with 0<=alpha<=180 degrees is 180 degrees-alpha. When measured in radians, it is pi-alpha. The only angle supplementary to itself is the right angle 90 degrees=pi/2 radians.

Supplementary angles need not be adjacent. If the two angles are adjacent, they form a linear pair. Each pair of opposite angles of a cyclic quadrilateral is also supplementary.

The illustration gives an adjacent realization. It shows the adjacent angles alpha=∠AOB and beta=∠BOC, which together form the straight angle ∠AOC.


See also

Angle, Complementary Angles, Cyclic Quadrilateral, Digon, Linear Pair, Straight Angle Explore this topic in the MathWorld classroom

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References

Hadamard, J. Lessons in Geometry, I: Plane Geometry. Providence, RI: Amer. Math. Soc., 2008.Rusczyk, R. Introduction to Geometry, 2nd ed. Alpine, CA: AoPS Inc., pp. 21-23, 2007.

Referenced on Wolfram|Alpha

Supplementary Angles

Cite this as:

Weisstein, Eric W. "Supplementary Angles." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/SupplementaryAngles.html

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