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