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Answer:
[tex]\text{ One of the exterior angles is 204}\degree[/tex]Step-by-step explanation:
The interior angles of any polygon are represented by the following equation:
[tex](n-2)\cdot180=\sum \text{interior}[/tex]If the sum of the interior angles is 2340, solve for n to determine how many vertices it has:
[tex]\begin{gathered} (n-2)\cdot180=2340 \\ n-2=\frac{2340}{180} \\ n=13+2 \\ n=15 \end{gathered}[/tex]Now, if the polygon has 15 vertices. Use the equation for the sum of exterior angles, which is represented as:
[tex]\begin{gathered} (n+2)\cdot180 \\ =(15+2)\cdot180 \\ =17\cdot180 \\ =3060 \end{gathered}[/tex]If it is a regular polygon, each angle measures the same:
[tex]\begin{gathered} \frac{3060}{15}=204\degree \\ \text{ One of the exterior angles is 204}\degree \end{gathered}[/tex]
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