Question

Given the sum of the interior angle measures, find the number of sides. NUMBER 11

Answer 1

So,

To find the number of sides of the polygon, we could use the fact that:

The formula for calculating the sum of interior angles is ( n − 2 ) × 180 where n is the number of sides. All the interior angles in a regular polygon are equal.

Given that the sum of all the internal angles is 1620, We could write the following equation and then solve for n as follows:

`\begin{gathered} 1620=(n-2)\cdot180 \\ 1620=180n-360 \\ 1620+360=180n \\ 1980=180n \\ n=11 \end{gathered}`

Therefore, the number of sides is 11.