Answer
m of an interior angle = $157.5$
m of an exterior angle = $22.5$
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 16-gon has 16 sides, so we plug this information into the formula to find the measure of one of its interior angles:
m of an interior angle = $\frac{(16 - 2)(180)}{16}$
Evaluate parentheses first:
m of an interior angle = $\frac{(14)(180)}{16}$
Multiply first:
m of an interior angle = $\frac{2520}{16}$
Divide to solve:
m of an interior angle = $157.5$
The measure of the exterior angle is just the measure of the interior angle subtracted from $180^{\circ}$:
m of an exterior angle = $180 - 157.5$
Subtract to solve:
m of an exterior angle = $22.5$
