Question

The exterior angle of a regular polygon is one third of its interior angle. The number of the sides of the polygon is:

Answer 1

angle (interior) of a polygon (n side)

is $\theta =\left(\frac{n-2}{n}\right){180}^{\circ }$

$\therefore$ exterior angle $={180}^{\circ }-\theta$

Given $\frac{{180}^{\circ }-\theta }{\theta }=\frac{1}{3}\Rightarrow \frac{[1-\left(\frac{n-2}{n}\right)]{180}^{\circ }}{\left(\frac{n-2}{n}\right)180}=\frac{1}{3}$

$\Rightarrow \frac{2}{n-2}=\frac{1}{3}\Rightarrow n=8$