Question

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

Answer 1

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 \(n\).

Answer 2

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