Question

The interior angle of a regular polygon exceeds the exterior angle by ${132}^{\circ }$. The number of sides in the polygon is

• A. 7
• B. 8
• C. 12
• D. 15

Answer 1

The correct option is D 15

Interior angle of polygon = $\frac{180(n-2)}{n}$
Exterior angle of a polygon = $\frac{360}{n}$
$\frac{180(n-2)}{n}-\frac{360}{n}=132$
$180n-360-360=132n$
$48n=720$
$n=\frac{720}{48}$
$n=15$