Question

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

• A. ${150}^{\circ }$
• B. ${140}^{\circ }$
• C. ${180}^{\circ }$
• D. ${120}^{\circ }$

Answer 1

The correct option is A ${150}^{\circ }$

The measure of each interior angle of a regular polygon is five times the measure of its exterior angle.
Each Interior angle of a polygon = $\frac{{180}^o(n-2)}{n}$
Each Exterior angle of a polygon = $\frac{{360}^o}{n}$
$\therefore \frac{{180}^o(n-2)}{n}=5\times \frac{{360}^o}{n}$
$=>n-2=10$
$=>n=12$
Number of sides of polygon is 12.
Each Interior angle of a polygon = $\frac{{180}^o(n-2)}{n}=\frac{{180}^o(12-2)}{12}={150}^o$