Question

An angle is equal to its supplement. What is its magnitude?

Answer 1

We know that If the sum of the two angles is $180°$, the angles are said to be supplementary angles and each angle said to be the supplement of the other.

Let $\mathrm{x}°$ be an angle.

Then, the supplement of $\mathrm{x}°$ is $180°-\mathrm{x}°$.

Given,

$$\begin{gathered} \mathrm{x}°=180°-\mathrm{x}° \\ \Rightarrow \mathrm{x}°+\mathrm{x}°=180° \\ \Rightarrow 2\mathrm{x}°=180° \\ \Rightarrow \mathrm{x}°=\frac{180°}{2} \\ \Rightarrow \mathrm{x}°=90° \end{gathered}$$

Hence, the required angle is $90°$.