# Sum of the interior angles of a polygon is 3060^@. How many sides does it have?

Jan 9, 2017

The interior angle sum is $\left(n - 2\right) \times {180}^{o}$, where n is the number of interior angles.

#### Explanation:

So triangle $\left(3 - 2\right) \times {180}^{o} = {180}^{o}$,
Quadrangle $\left(4 - 2\right) \times {180}^{o} = {360}^{o}$,
Etc.

$\left(n - 2\right) \times {180}^{o} = {3060}^{o} \to n - 2 = {3060}^{o} / {180}^{o} = 17 \to n = 19$

This is also the number of sides.