Question

I. Given: a regular 18 sided convex polygon

a. Find the measure of an interior angle.


b. Find the sum of the measures of the interior angles.


c. Find the measure of an exterior angle.

Answer 1

(c) is the easiest. The exterior angles of a regular convex polygon add up to 360 degrees. Since they're all equivalent, the measure of each exterior angle is \(\dfrac{360}{18}\) degrees.

Exterior and interior angles are supplementary, so \(\angle(\text{ext})+\angle(\text{int})=180^\circ\). This means each interior angle is \(180-\dfrac{360}{18}\) degrees.

The sum of the interior angles is then \(18\left(180-\dfrac{360}{18}\right)\) degrees, since there are 18 interior angles.