Chapter 6.1, Problem 23PPS

To determine

The measure of each interior angle of each regular polygon.

Answer to Problem 23PPS

The measure of each interior angle of the given polygon is 144.

Explanation of Solution

Given:

The given polygon is decagon.

Calculation:

The sum of the measures of interior angles of an n-sided polygon is:

  $\left(n-2\right)180$

Decagon has 10 sides.

So, put the value in the formula:

  $\begin{array}{l}Sum=\left(n-2\right)180\\ Sum=\left(10-2\right)180\\ Sum=\left(8\right)180\\ Sum=1440\end{array}$

As the given polygon is a regular 10-gon, the interior angles are congruent.

Calculating the measure of one interior angle:

  $\begin{array}{l}\frac{\text{Sum of interior angle measures}}{\text{Number of congruent angles}}=\frac{1440}{10}\\ \text{ =144}\end{array}$

Therefore, the measure of each interior angle of the given polygon is 144.