Question

If the exterior angle of a regular polygon equals $120$ degrees, what shape is the polygon?

Answer 1

Find the shape of the polygon:

The sum of exterior angle of a regular polygon is ${360}^{\circ }$.

We know that, if there are $n$ sides of regular polygon then measure of each exterior angle is given by $\left(\frac{360}{n}\right)°$.

Given that exterior angle of a regular polygon equals $120°$ , so we have

$\begin{array}{rcl}\frac{360}{n}& =& 120\\ & \Rightarrow & \frac{n}{360}=\frac{1}{120}\left(\mathrm{Taking}\mathrm{reciprocal}\mathrm{of}\mathrm{both}\mathrm{sides}\right)\\ & \Rightarrow & n=\frac{360}{120}\left(\mathrm{Multiplying}\mathrm{both}\mathrm{sides}\mathrm{by}360\right)\\ \therefore n& =& 3\end{array}$

The number of sides are $3$.

Polygon with three sides is a triangle.

Hence, the shape of the polygon is triangle.