Question

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

• A. 12
• B. 13
• C. 14
• D. 15

Answer 1

The correct option is D 15

In question we have given difference between interior angle and exterior angle is 132${}^{\circ }$

Let $I$ is interior angle and $E$ be exterior angle then we get,

$I-E$ = ${132}^{\circ }$ --- (1) (Given)

$I+E$ = ${180}^{\circ }$ --- (2) (Linear pair)

Adding equation (1) and (2) we get,

$2I$ = ${180}^{\circ }+{132}^{\circ }$

$2I$ = ${312}^{\circ }$

$\therefore$ $I={156}^{\circ }$

$\Rightarrow$ $E={180}^{\circ }-{156}^{\circ }={24}^{\circ }$

$\therefore$ Number of sides of polygon = $\frac{{360}^{\circ }}{{24}^{\circ }}$ = $15$.