Sullivan Mathis
09/28/2023 · Senior High School
(S points) What is the measure of an exterior angle of a regular 9-sided polygon? Show all your work.
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Step-by-step Solution
To find the measure of an exterior angle of a regular polygon, we can use the formula:
\[
\text{Exterior angle} = \frac{360^\circ}{n}
\]
where \( n \) is the number of sides of the polygon. In this case, we have a regular 9-sided polygon (also known as a nonagon).
1. Identify \( n \):
\[
n = 9
\]
2. Substitute \( n \) into the formula:
\[
\text{Exterior angle} = \frac{360^\circ}{9}
\]
3. Perform the division:
\[
\text{Exterior angle} = 40^\circ
\]
Thus, the measure of an exterior angle of a regular 9-sided polygon is
\[
\boxed{40^\circ}
\]
Quick Answer
The measure of an exterior angle of a regular 9-sided polygon is \( 40^\circ \).
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