Question

A regular polygon with each exterior angle = ${40}^{\circ }$ is a

• A. nonagon
• B. decagon
• C. octagon

Answer 1

The correct option is A nonagon

Sum of external angles of any polygon is ${360}^{\circ }$
Since it is a regular polygon, all the exterior angles are equal i.e., ${40}^{\circ }$ each.
Exterior angle = $\frac{360°}{n}$; where n is the number of sides.
$\Rightarrow$ n =$\frac{360°}{40°}$
$\Rightarrow$ n = 9
Hence, the regular polygon whose exterior angle is ${40}^{\circ }$ is a nonagon.