Question

If the interior angle of a regular polygon is equal to the exterior angle, the number of sides in the polygon is

• A. 5
• B. 6
• C. 4
• D. 7

Answer 1

The correct option is C

4

For any polygon, interior angle + exterior angle = ${180}^{\circ }$

$\Rightarrow i+e={180}^{\circ }$

$\Rightarrow 2e={180}^{\circ }$ [$\because$ interior angle is equal to the exterior angle]

$\Rightarrow e={90}^{\circ }$

Now,

Number of sides of a polygon $\left(n\right)=\frac{{360}^{\circ }}{e}$

$\Rightarrow \left(n\right)=\frac{{360}^{\circ }}{{90}^{\circ }}$

$\Rightarrow \left(n\right)=4$