Chapter 6.1, Problem 4CYU

To determine

The measures of each interior angle in the given figure.

Answer to Problem 4CYU

  $\begin{array}{l}m\angle A=122°\\ m\angle B=112°\\ m\angle C=112°\\ m\angle D=117°\\ m\angle E=126°\\ m\angle F=116°\end{array}$

Explanation of Solution

Given:

The given figure is:

Calculation:

The sum of interior angles on an n-sided convex polygon is $\left(n-2\right)·180.$

The given figure is a 6-gon, therefore;

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

Therefore;

  $\begin{array}{l}m\angle A+m\angle B+m\angle C+m\angle D+m\angle E+m\angle F=720°\\ x+2+x-8+x+7+x-3+x+6+x-4=720°\\ 6x=720°\\ x=120°\end{array}$

Finding the value of all the angles:

The measure of angle A is:

  $\begin{array}{l}m\angle A=x+2\\ m\angle A=120+2\\ m\angle A=122\end{array}$

The measure of angle B is:

  $\begin{array}{l}m\angle B=x-8\\ m\angle B=120-8\\ m\angle B=112\end{array}$

The measure of angle C is:

  $\begin{array}{l}m\angle C=x+7\\ m\angle C=120+7\\ m\angle C=127\end{array}$

The measure of angle D is:

  $\begin{array}{l}m\angle D=x-3\\ m\angle D=120-3\\ m\angle D=117\end{array}$

The measure of angle E is:

  $\begin{array}{l}m\angle E=x+6\\ m\angle E=120+6\\ m\angle E=126\end{array}$

The measure of angle F is:

  $\begin{array}{l}m\angle F=x-4\\ m\angle F=120-4\\ m\angle F=116\end{array}$