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Complementary Angles


ComplementaryAngles

Complementary angles are two angles alpha and beta whose measures satisfy alpha+beta=90 degrees, the measure of a right angle. Equivalently, their measures sum to pi/2 radians.

When measured in degrees, the complement of an angle alpha with 0<=alpha<=90 degrees is 90 degrees-alpha. When measured in radians, it is pi/2-alpha. The only angle complementary to itself is 45 degrees=pi/4 radians. The two acute angles of a right triangle are complementary.

Complementary angles need not be adjacent. The illustration gives an adjacent realization. It shows the adjacent angles alpha=∠AOB and beta=∠BOC, which together form the right angle ∠AOC.


See also

Acute Angle, Angle, Right Angle, Right Triangle, Supplementary Angles 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

Complementary Angles

Cite this as:

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

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