Question

The ratio of an interior angle to the exterior angle of a regular polygon is $7:2$. Find the number of sides of the polygon.

• A. $9$
• B. $19$
• C. $7$
• D. $8$

Answer 1

Answer: (A)

$9$

Interior angle of a polygon of $n$-sides $=$ $\frac{(n-2)\pi }{n}$

Exterior angle of a polygon of $n$-sides $=$ $\frac{2\pi }{n}$

Taking there ratio, and equating it to $\frac{7}{2}$

Thus $\frac{n-2}{2}$ $=$ $\frac{7}{2}$

$\Rightarrow n=9$