Question

The ratio between an exterior angle and an interior angle of a regular polygon is $2:3$. Find the number of sides in the polygon.

• A. $5$
• B. $7$
• C. $2$
• D. $11$

Answer 1

The correct option is A $5$

The ratio between the exterior angle and interior angle of a regular polygon is $2:3$.
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,
$\frac{{360}^o}{n}:\frac{{180}^o(n-2)}{n}=2:3$
$=>\frac{2}{(n-2)}=\frac{2}{3}$
$=>n-2=3$
$=>n=5$