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Expert-verified Found in: Page 700 ### Pre-algebra

Book edition Common Core Edition
Author(s) Ron Larson, Laurie Boswell, Timothy D. Kanold, Lee Stiff
Pages 183 pages
ISBN 9780547587776 # Find the measure of an exterior angle of a regular pentagon.

The measure of an exterior angle of a regular pentagon is $72°$.

See the step by step solution

## Step 1. Given Information.

The polygon is regular pentagon.

## Step 2. Formula used.

All exterior angles of a regular polygon are equal and the measure of an exterior angle of regular n-gon, is $180{}^{\circ }-\frac{\left(n-2\right)×180°}{n}$.

## Step 3. Calculation.

Here, polygon is regular pentagon that is $n=5$.

Calculate the measure of the exterior angle by substituting 5 for n.

$\begin{array}{c}180°-\frac{\left(5-2\right)×180°}{5}=180°-\frac{3×180°}{5}\\ =180°-108°\\ =72°\end{array}$

## Step 4. Conclusion.

The measure of an exterior angle of a regular pentagon is $72°$. ### Want to see more solutions like these? 