Definition:Supplementary Angles



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, which, when set next to each other, form a straight angle are supplementary.

Compare To

 * Complementary