Question

The measure of each interior angle of a regular polygon is five times the measure of its exterior angle. Find the number of sides in the polygon

• A. $12$
• B. $18$
• C. $24$
• D. $36$

Answer 1

Answer: (A)

$12$

Given the measure of each interior angle of a regular polygon is five times the measure of its exterior angle.
Each interior angle of a regular polygon = $\frac{{180}^o(n-2)}{n}$ where $n$ = number of sides of polygon
Each exterior angle of a regular polygon = $\frac{{360}^o}{n}$
According to question,
$\frac{{180}^o(n-2)}{n}=5\times \frac{{360}^o}{n}$
$=>n-2=10$
$=>n=12$
Number of sides of the polygon $=12$