Question

The ratio between the interior angle and the exterior angle of a regular polygon is $2:1$, find number of sides in the polygon.

• A. $5$
• B. $6$
• C. $7$
• D. $8$

Answer 1

The correct option is B $6$

The ratio between the interior angle and the exterior angle of a regular polygon is $2:1$.
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,
$\frac{{180}^o(n-2)}{n}:\frac{{360}^o}{n}=2:1$
$=>\frac{(n-2)}{2}=\frac{2}{1}$
$=>n-2=4$
$=>n=6$
Number of sides of the polygon $=6$