Question

Find the number of sides in a regular polygon, if its interior angle is equal to its exterior angle.

• A. $1$
• B. $5$
• C. $2$
• D. $4$

Answer 1

Answer: (D)

$4$

A regular polygon, whose interior angle is equal to its exterior angle.
Each Interior angle of a polygon = $\frac{{180}^o(n-2)}{n}$
Each Exterior angle of a polygon = $\frac{{360}^o}{n}$
$\therefore \frac{{180}^o(n-2)}{n}=\frac{{360}^o}{n}$
$=>n-2=2$
$=>n=4$
Number of sides of polygon is $4$.