Question

The sum of the interior angles of a polygon with n sides is 1980°. Find n.

Answer 1

We can relate the sum of the interior angles of a polygon S with its number of sides n as:

$S=(n-2)\cdot180$

Then, if S=1980 degrees, we can find n as:

$\begin{gathered} 1980=(n-2)\cdot180 \\ n-2=\frac{1980}{180} \\ n-2=11 \\ n=11+2 \\ n=13 \end{gathered}$

Answer: the polygon has 13 sides (n=13)