Chapter 6, Problem 8STP

To determine

The measure of the angle formed at each corner of gazebo.

Answer to Problem 8STP

The measure of each angle formed at the corners is 120.

Explanation of Solution

Given:

The polygon is a hexagon.

Calculation:

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

  $\left(n-2\right)180$

The sides in a hexagon are 6.

So, put the value in the formula:

  $\begin{array}{l}Sum=\left(n-2\right)180\\ Sum=\left(6-2\right)180\\ Sum=\left(4\right)180\\ Sum=720\end{array}$

The sum of the measures of interior angles of a hexagon is 720.

As the object is a regular 6-gon, all of its interior angles are congruent.

Calculating the measure of one interior angle:

  $\begin{array}{l}\frac{\text{Sum of interior angle measures}}{\text{Number of congruent angles}}=\frac{720}{6}\\ \text{ =120}\end{array}$

The measure of each angle formed at the corners is 120.