Question

An angle is $\frac{2}{3}$ of its supplementary. What is its magnitude?

Answer 1

$\Rightarrow$ Let one angle be $x$.

$\Rightarrow$ Then, other angle will be $\frac{2}{3}x$

According to the question,

$x+\frac{2}{3}x={180}^o$

$\frac{3x+2x}{3}={180}^o$

$\frac{5x}{3}={180}^o$

$5x={540}^o$

$\therefore$ $x={108}^o$

$\therefore$ $\frac{2}{3}x=\frac{2}{3}\times {108}^o={72}^o$

$\therefore$ Magnitudes are ${108}^o$ and ${72}^o$