Question

Find the number of sides in a regular polygon , if its each exterior angle is :(ii) ${36}^{\circ }$.

Answer 1

Let the number of sides be $n$.
Given : Each exterior angle is ${36}^{\circ }$
Each exterior angle $=\frac{{360}^{\circ }}{n}$
$\therefore {36}^{\circ }=\frac{{360}^{\circ }}{n}$
$\Rightarrow n=\frac{{360}^{\circ }}{{36}^{\circ }}$
$\therefore n=10$
Hence, the required number of sides is $10$.