Question

Find the number of sides of a regular polygon whose each exterior angles has a measure of
${72}^{\circ }$

Answer 1

Let us assume the number of sides of the regular polygon be $n$,

Sum of all exterior angles is ${360}^o$.
$\begin{array}{c}\text{Then,}n=\frac{{360}^{\circ }}{{72}^{\circ }}\\ n=5\end{array}$
Therefore, the number of sides of a regular polygon is $5$