Question

How many sides does a regular polygon have if the measure of an exterior angle is ${24}^0$?

• A. $14$
• B. $13$
• C. $15$
• D. $18$

Answer 1

Answer: (C)

$15$

Here, let the number of sides of the polygon be $n$

So, the number of exterior angles is $n$

Since it is a regular polygon, each exterior angles are equal to one another.

$\therefore$ The sum of the exterior angles $={360}^o$

$\therefore$ Each angle $=\theta =\frac{{360}^o}{n}$

$⟹n=\frac{{360}^o}{\theta }$

Here $\theta ={24}^o$

$\therefore n=\frac{{360}^o}{{24}^o}=15$

Hence, the answer is $15$.