Question

The number of sides in a regular polygon having measure of an exterior angle as ${72}^0$ is __________.

Answer 1

We know that the measure of each exterior angle of a regular pentagon is$\frac{{360}^o}{n}$, where $‘n’$ is the number of sides in the polygon,

The pentagon has exterior angle $={72}^o$

So,${72}^o=\frac{{360}^o}{n}$

$$\begin{gathered} n=\frac{{360}^o}{{72}^0} \\ n=5 \end{gathered}$$

Hence, the number of sides is $5$.