Question
Find an angle whose supplement is $\frac{2}{3}$ of it.
✓
Answer
Let $x$ be an angle, whose supplement is $\frac{2}{3}$ of it.
We know that sum of supplementary angles is $180^{\circ}$.
$\begin{aligned}\text { So, } x+\frac{2}{3} x =180^{\circ} \\
\frac{3 x+2 x}{3}=180^{\circ} \Rightarrow \frac{5 x}{3}=180^{\circ} \\
\Rightarrow x=\frac{180^{\circ} \times 3}{5}=36^{\circ} \times 3=108^{\circ} \\
\Rightarrow x=108^{\circ}
\end{aligned}
$
We know that sum of supplementary angles is $180^{\circ}$.
$\begin{aligned}\text { So, } x+\frac{2}{3} x =180^{\circ} \\
\frac{3 x+2 x}{3}=180^{\circ} \Rightarrow \frac{5 x}{3}=180^{\circ} \\
\Rightarrow x=\frac{180^{\circ} \times 3}{5}=36^{\circ} \times 3=108^{\circ} \\
\Rightarrow x=108^{\circ}
\end{aligned}
$
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