# The sum of the measures of the interior angles of a convex polygon is 540. How do you classify the polygon by the number of sides?

Aug 27, 2017

Polygon is a pentagon i.e. $5$ sides.

#### Explanation:

If $n$ are number of sides of a convex polygon, sum of its interior angles is $\left(n - 2\right) \times {180}^{\circ}$

As in given case sum of interior angles is ${540}^{\circ}$, we have

$\left(n - 2\right) \times {180}^{\circ} = {540}^{\circ}$

or $n - 2 = \frac{540}{180} = 3$

and $n = 3 + 2 = 5$

Hence, polygon is a pentagon.