How many sides does a regular polygon have if the measure of an exterior angle...

To determine the number of sides, use the polygon's exterior angle sum property:
It is given that a regular polygon has the measure of an exterior angle $24°$.
Since according to the exterior angle sum property of the polygon,
(number of sides) $\times$(the measure of each exterior angle) $=360°$[Using exterior angle property]
$\Rightarrow$ (number of sides) $\times$$24°=360°$
$\Rightarrow$ Number of sides $=\frac{360°}{24°}$
$\Rightarrow$$=15$
Hence, the polygon has $15$sides.