Question

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

• A. ${40}^{\circ }$
• B. ${50}^{\circ }$
• C. ${30}^{\circ }$
• D. ${45}^{\circ }$

Answer 1

Answer: (C)

${30}^{\circ }$

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,

$\frac{{180}^o(n-2)}{n}=5\times \frac{{360}^o}{n}$

$\Rightarrow n-2=10$

$\Rightarrow n=12$

Each exterior angle of a regular polygon = $\frac{{360}^o}{n}=\frac{{360}^o}{12}={30}^o$