Question

If the interior angle of a regular polygon exceeds the exterior angle by ${132}^{\circ }$, then the number of sides of the polygon is :

• A. $15$
• B. $14$
• C. $13$
• D. $12$

Answer 1

The correct option is A $15$

Let the number of sides in the regular polygon be $n$

Thus each interior angle $=$ $\frac{(2n-4)\times {90}^{\circ }}{n}$

And each exterior angle $=\frac{{360}^{\circ }}{n}$

Lets go according to question:

Therefore, $\frac{(2n-4)\times {90}^{\circ }}{n}-\frac{{360}^{\circ }}{n}={132}^{\circ }$

$\Rightarrow 180n-360-360=132n$

$\Rightarrow 48n=720$

$\Rightarrow n=\frac{720}{48}=15$