Question

An exterior angle and an interior angle of a regular polygon are in the ratio $2:7$. Find the number of sides in the polygon.

• A. $2$
• B. $7$
• C. $9$
• D. $18$

Answer 1

Answer: (C)

$9$

Exterior angle $=\frac{{360}^{\circ }}{n}$ (n is number of sides of a polygon)

Interior angle $=\frac{(n-2){180}^{\circ }}{n}$

$\Rightarrow \frac{2}{7}=\frac{{360}^{\circ }}{(n-2){180}^{\circ }}$

$\Rightarrow n-2=7$

$\Rightarrow n=9$

Hence, the number of sides in the polygon is $9$.