# How many sides are in a polygon whose sum of the interior angles is 1440?

Sep 10, 2016

There are 10 sides.

#### Explanation:

If you draw triangles inside a polygon using one vertex and joining it to all the other vertices (without line crossing) the number of triangles will be 2 less than the number of sides . Hence $\left(n - 2\right)$ in the formula. Each triangle has 180°.

$1440 \div 180$ will give the number of triangles.

Then add 2 to find the number of sides.

$1441 \div 180 = 8$triangles

$8 + 2 = 10 \text{ sides}$

Or you could use the formula, it does exactly the same process.

$180 \left(n - 2\right) = 1440$

$n - 2 = \frac{1440}{18} = 8$

$n = 8 + 2 = 10$