# If the sum of the measures of the interior angles of a polygon is 5400°, how many sides does it have?

Apr 11, 2017

$32$

#### Explanation:

Let $S$ be the sum of the interior angles of the polygon,

$\implies S = \left(n - 2\right) \cdot {180}^{\circ}$,
where $n$ is the number of sides.

Given $S = {5400}^{\circ}$
$\implies 5400 = \left(n - 2\right) \cdot 180$
$\implies n - 2 = \frac{5400}{180} = 30$
$\implies n = 32$

Hence, the polygon has 32 sides.