Question

Exterior angle of a regular polygon is ${45}^o.$ What type of polygon is it?

• A. Hexagon
• B. Septagon
• C. Octagon
• D. Pentadecagon

Answer 1

The correct option is C Octagon

We know that the sum of all exterior angles of any polygon is ${360}^o.$

A regular polygon has equal interior angles, hence equal exterior angles.

Let the polygon as $n$ sides.

Measure of each exterior angle $=\frac{{360}^o}{n}$
$\Rightarrow {45}^o=\frac{{360}^o}{n}$
$\Rightarrow n=\frac{{360}^o}{{45}^o}=8$

Hence, the polygon has $8$ sides, i.e., an octagon.