# Definition:Supplementary Angles

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## Definition

Let $\angle ACB$ be a straight angle.

Let $\angle BCD + \angle DCA = \angle ACB$.

That is, $\angle DCA = \angle ACB - \angle BCD$.

Then $\angle DCA$ is the supplement of $\angle BCD$.

Hence, for any angle $\alpha$ (whether less than a straight angle or not), the supplement of $\alpha$ is $\pi - \alpha$.

Measured in degrees, the supplement of $\alpha$ is $180^\circ - \alpha$.

If $\alpha$ is the supplement of $\beta$, then it follows that $\beta$ is the supplement of $\alpha$.

Hence we can say that $\alpha$ and $\beta$ are supplementary.

It can be seen from this that the supplement of a reflex angle is negative.

Thus, supplementary angles are two angles whose measures add up to the measure of two right angles.

That is, their measurements add up to $180$ degrees or $\pi$ radians.

Another (equivalent) definition is to say that two angles are supplementary which, when set next to each other, form a straight angle.

## Also known as

Some sources use the term adjacent angles for this concept, but $\mathsf{Pr} \infty \mathsf{fWiki}$ has a different definition for that term.