Chapter 6.1, Problem 19PPS

To determine

The measures of each interior angle in the given figure.

Answer to Problem 19PPS

  $\begin{array}{l}m\angle U=60°\\ m\angle V=193°\\ m\angle W=76°\\ m\angle Y=68°\\ m\angle Z=143°\end{array}$

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;

  $\begin{array}{l}m\angle U+m\angle V+m\angle W+m\angle Y+m\angle Z=540°\\ \left(x-8\right)+\left(3x-11\right)+\left(x+8\right)+x+\left(2x+7\right)=540\\ 8x-4=540\\ 8x=544\\ x=68\end{array}$

Finding the value of all the angles:

The measure of angle U is:

  $\begin{array}{l}m\angle U=x-8\\ m\angle U=68-8\\ m\angle U=60\end{array}$

The measure of angle V is:

  $\begin{array}{l}m\angle V=3x-11\\ m\angle V=3\left(68\right)-11\\ m\angle V=204-11\\ m\angle V=193\end{array}$

The measure of angle W is:

  $\begin{array}{l}m\angle W=x+8\\ m\angle W=68+8\\ m\angle W=76\end{array}$

The measure of angle Y is:

  $\begin{array}{l}m\angle Y=x\\ m\angle Y=68\end{array}$

The measure of angle Z is:

  $\begin{array}{l}m\angle Z=2x+7\\ m\angle Z=2\left(68\right)+7\\ m\angle Z=143\end{array}$