Question

Complete.

10. In a regular decagon, the sum of the measures of the exterior angles is$\underset{¯}{?}$ and the measure of each interior angle is $\underset{¯}{?}$.

Short answer

In a regular decagon, the sum of the measures of the exterior angles is360°and the measure of each interior angle is144°.

Step-by-step solution

Step 1. Description of step.

In a decagon, the number of sides are 10.

Therefore, the value of n is 10.

Step 2. Description of step.

The sum of the measures of exterior angles of a polygon is360°.

Therefore, the sum of the measures of exterior angles of a decagon is 360°.

Step 3. Description of step.

The measure of each interior angle of a regular polygon with n sides is given by $\frac{\left(n-2\right)180°}{n}$.

Therefore, the measure of each interior angle of a regular polygon with 10 sides is given by:

$\begin{array}{c}\frac{\left(10-2\right)180°}{10}=\frac{8\times 180°}{10}\\ =8\times 18°\\ =144°\end{array}$

Step 4. Write the complete statement.

In a regular decagon, the sum of the measures of the exterior angles is 360° and the measure of each interior angle is 144°.