One exterior angle of a regular polygon measures 30. What is the sum of the polygon's interior angle measures?

Dec 22, 2015

The explanation with the solution is given below.

Explanation:

Exterior angle of $n$ sided regular polygon is found by the formula

$\frac{360}{n}$

We are given one exterior angle is ${30}^{o}$

$\frac{360}{n} = 30$

$\implies n = \frac{360}{30}$

$\implies n = 12$

The polygon is a dodecagon.

The sum of the interior angles is found by the formula

$\left(n - 2\right) \cdot {180}^{o}$

Here we found the number of sides is 12, therefore $n = 12$

$\left(12 - 2\right) \cdot {180}^{o}$

$= 10 \cdot {180}^{o}$

$= {1800}^{o}$ Answer