Chapter 6.1, Problem 18PPS

To determine

The measures of each interior angle in the given figure.

Answer to Problem 18PPS

  $\begin{array}{l}m\angle A=90°\\ m\angle B=90°\\ m\angle C=128°\\ m\angle D=74°\\ m\angle E=158°\end{array}$

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 5-gon, therefore;

  $\begin{array}{l}Sum=\left(n-2\right)180\\ Sum=\left(5-2\right)180\\ Sum=540\end{array}$

Therefore;

  $\begin{array}{l}m\angle A+m\angle B+m\angle C+m\angle D+m\angle E=540°\\ 90+90+\left(2x-20\right)+x+\left(2x+10\right)=540\\ 5x+170=540\\ 5x=370\\ x=74\end{array}$

Finding the value of all the angles:

The measure of angle C is:

  $\begin{array}{l}m\angle C=2x-20\\ m\angle C=2\left(74\right)-20\\ m\angle C=148-20\\ m\angle C=128\end{array}$

The measure of angle D is:

  $\begin{array}{l}m\angle D=x\\ m\angle D=74\end{array}$

The measure of angle E is:

  $\begin{array}{l}m\angle E=2x+10\\ m\angle E=2\left(74\right)+10\\ m\angle E=148+10\\ m\angle E=158\end{array}$