Question

The ratio between the interior and the exterior angle of a regular polygon is $2:1$.Find:
$\left(ii\right)\text{Number of sides in the polygon}$

Answer 1

Given: Ratio between interior angle and exterior angle $=2:1$

Let interior angle $\text{=2x}$ and exterior angle $=x$

Now, exterior angle $+$ interior angle $={180}^{\circ }$

$\Rightarrow x+2x={180}^{\circ }$

$3x={180}^{\circ }$

$\therefore x={60}^{\circ }$

Hence, the exterior angle is ${60}^{\circ }$.

Find number of sides

Let the number of sides in the polygon be $n$

Each exterior angle $=\frac{{360}^{\circ }}{n}$

${60}^{\circ }=\frac{{360}^{\circ }}{n}$

$n=\frac{{360}^{\circ }}{{60}^{\circ }}$

$\therefore n=6$

Hence, the number of sides in a polygon whose exterior angle is ${60}^{\circ }$ is $6$.