Question

The magnitude of an angle which is $\frac{2}{3}$ of its supplement.

Answer 1

Let one angle is $x$.

Then, its supplementary angle is $({180}^{\circ }-x)$.

According to the question, we have

One angle $=\frac{2}{3}\times$ Its Supplement

$\Rightarrow x=\frac{2}{3}({180}^{\circ }-x)$

$\Rightarrow 3x=2\times {180}^{\circ }-2x$

$\Rightarrow 5x=2\times {180}^{\circ }$

$\Rightarrow x=\frac{2\times {180}^{\circ }}{5}={72}^{\circ }$

Hence, the magnitude of an angle which is $\frac{2}{3}$ of its supplement is ${72}^{\circ }$