Question

An angle is $\frac{2}{3}$ of 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,

$$\begin{gathered} \mathrm{x}°=\frac{2}{3}\left(180°-\mathrm{x}°\right) \\ \Rightarrow 3\mathrm{x}°=2\left(180°-\mathrm{x}°\right) \\ \Rightarrow 3\mathrm{x}°=360°-2\mathrm{x}° \\ \Rightarrow 3\mathrm{x}°+2\mathrm{x}°=360° \\ \Rightarrow 5\mathrm{x}°=360° \\ \Rightarrow \mathrm{x}°=\frac{360°}{5} \\ \Rightarrow \mathrm{x}°=72° \end{gathered}$$

Hence, the required angle is $72°$.