Answer
m of an interior angle = $108$
m of an exterior angle = $72$
Work Step by Step
The measure of an interior angle of a polygon is given by the following formula:
m of an interior angle = $\frac{(n - 2)(180)}{n}$, where $n$ is the number of sides in the polygon.
A pentagon has 5 sides, so we plug this information into the formula to find the measure of one of its interior angles:
m of an interior angle = $\frac{(5 - 2)(180)}{5}$
Evaluate parentheses first:
m of an interior angle = $\frac{(3)(180)}{5}$
Multiply first:
m of an interior angle = $\frac{540}{5}$
Divide to solve:
m of an interior angle = $108$
The measure of the exterior angle is just the measure of the interior angle subtracted from $180^{\circ}$:
m of an exterior angle = $180 - 108$
Subtract to solve:
m of an exterior angle = $72$
