Question

The regular polygon whose exterior angle is ${40}^{\circ }$ is a:

• A. Nonagon
• B. Decagon
• C. Octagon
• D. Heptagon

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
It is a nonagon.