Definition:Supplementary Angles
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 $180 \degrees - \alpha$.
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.
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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 $2$ 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 to mean supplementary angles, but $\mathsf{Pr} \infty \mathsf{fWiki}$ has a different definition for that term.
Also see
- Results about supplementary angles can be found here.
Sources
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): supplement
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): supplementary angles
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): supplement
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): supplementary angles