The sum of the measures of the interior angles of a regular polygon is 1980. Find the number of sides in the polygon.

Question

anonymous · Answer

Sum of exterior angles is 360 degrees.

Any one exterior angle would be $\dfrac{360}{n}$ degrees for a regular $n$-gon.

Exterior angles supplement interior angles, so any one interior angle would be $\left(180-\dfrac{360}{n}\right)$ degrees.

There are $n$ interior angles to an $n$-gon, so the sum would be $(180n-360)$ degrees.
$$180n-360=1980$$
Solve for $n$.

anonymous · Answer

ohhhh thanks bruh