If an exterior angle of a regular polygon measures 24°, how many sides does the polygon have?

Oct 29, 2016

The polygon has $15$ sides.

Explanation:

The formula for finding the measure of an exterior angle of a regular polygon is

$\frac{360}{n}$, where $n$ is the number of sides of the polygon. So,

$24 = \frac{360}{n}$

$24 \left(n\right) = n \left(\frac{360}{n}\right)$

$24 n = 360$
$\frac{24 n}{24} = \frac{360}{24}$

$n = 15$

So the polygon has $15$ sides.