Question

Is it possible to have a regular polygon whose each exterior angle is:
$\left(ii\right)$ $40\%$ of a right angle

Answer 1

Step: Recalling the concept of exterior angles of polygon

Let, number of sides of regular polygon $=n$

Given, each exterior angle $=40\%$ of a right angle.

$=\frac{40}{100}\times {90}^{\circ }$

$={36}^{\circ }$

$\therefore \frac{{360}^{\circ }}{n}={36}^{\circ }$

[$\because$ If a regular polygon has n sides, each exterior angle $=\frac{{360}^{\circ }}{n}$]

$\Rightarrow n=\frac{{360}^{\circ }}{{36}^{\circ }}=10$ (Which is a whole number)

Hence, it is possible to have a regular polygon whose exterior angle is $40\%$ of right angle.