Question

How many sides does a regular polygon have if the measure of an exterior angle is $24°$?

Answer 1

Use the exterior angle sum property of the polygon to find the number of sides:

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.