Question

Find the number of sides in a regular polygon, if its each interior angle is:​
$\left(i\right)$ ${160}^{\circ }$

Answer 1

Let number of sides of regular polygon be $n$

Given, Each interior angle $={160}^{\circ }$

$\therefore \frac{(n-2)}{n}\times {180}^{\circ }={160}^{\circ }$

[ $\because$ If a regular polygon has n sides, each interior angle $=\frac{(n-2)\times {180}^{\circ }}{n}$ ]

$\Rightarrow {180}^{\circ }n-{360}^{\circ }={160}^{\circ }n$

$\Rightarrow {180}^{\circ }n-{160}^{\circ }n={360}^{\circ }$

$\Rightarrow {20}^{\circ }n={360}^{\circ }$

$\Rightarrow n=18$

Hence, the number of sides of the given polygon is $18$