Question

Find the measure of one exterior angle of a regular polygon whose sum of the interior angles is 2340

Answer 1

`\text{ One of the exterior angles is 204}\degree`

Explanation:

The interior angles of any polygon are represented by the following equation:

`(n-2)\cdot180=\sum \text{interior}`

If the sum of the interior angles is 2340, solve for n to determine how many vertices it has:

`\begin{gathered} (n-2)\cdot180=2340 \\ n-2=(2340)/(180) \\ n=13+2 \\ n=15 \end{gathered}`

Now, if the polygon has 15 vertices. Use the equation for the sum of exterior angles, which is represented as:

`\begin{gathered} (n+2)\cdot180 \\ =(15+2)\cdot180 \\ =17\cdot180 \\ =3060 \end{gathered}`

If it is a regular polygon, each angle measures the same:

`\begin{gathered} (3060)/(15)=204\degree \\ \text{ One of the exterior angles is 204}\degree \end{gathered}`