Question

# How many sides does a regular polygon have if the measure of an exterior angle is${24^\circ }$ ?

We have to find the total number of sides of a regular polygon if the exterior angle is ${24^\circ }$
Let the number of sides of the polygon be $n$
Now if the number of sides of a regular polygon is $n$ then the number of exterior angles will also be $n$ only.
Now in a regular polygon, each exterior angle are equal to one another and sum of exterior angle is ${360^\circ }$
So we can say that $n\theta = {360^\circ }$
$\Rightarrow n = \frac{{{{360}^\circ }}}{\theta }$
Now $\theta = {24^\circ }$ Given in question
Hence $n = \frac{{{{360}^\circ }}}{{{{24}^\circ }}} = 15$
Note- Always remember while solving such problem statements that all the exterior angles of a regular polygon are equal and its sum is equal to${360^\circ }$. This concept will help you reach the right solution.