Question

The ratio between the exterior angle and interior angle of a regular polygon is $1:4$. Find the number of sides in the polygon.

• A. $8$
• B. $9$
• C. $10$
• D. $11$

Answer 1

The correct option is C $10$

The ratio between the exterior angle and interior angle of a regular polygon is $1:4$

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,

$\frac{{360}^o}{n}:\frac{{180}^o(n-2)}{n}=1:4$

$=>\frac{2}{(n-2)}=\frac{1}{4}$

$=>n-2=8$

$=>n=10$

Number of sides of the polygon $=10$