Question

If each exterior angle of a regular polygon measures ${36}^{\circ }$, then it has ___ sides.

• A. 9
• B. 10
• C. 11
• D. 12

Answer 1

The correct option is B

10

Given, exterior angle = ${36}^{\circ }$.

$\because$ Sum of exterior angles in a polygon = 360${}^{\circ }$

Since the polygon is regular all its sides and angles will be equal.

$\Rightarrow$ n $\times$ exterior angle = 360${}^{\circ }$ (where, n is the number of sides in the polygon)

$\Rightarrow n=\frac{{360}^{\circ }}{exteriorangle}$

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

= 10

$\therefore$ Number of sides of a regular polygon having exterior angle ${36}^{\circ }$ is 10.