Chapter 3.4, Problem 8WE

To determine

To find: The value of x for the given angles of the triangle.

Answer to Problem 8WE

The value of x for the given angles of the triangle is $x=50$ .

Explanation of Solution

Given information:

  

  $m\angle 6=x$ and $m\angle 7=x-20$ and $m\angle 11=80$

Calculation:

Considering the figure of a triangle provided

  $m\angle 6=x$ and $m\angle 7=x-20$ and $m\angle 11=80$

Since $\angle 11$ is an exterior angle of this triangle.

And it is known that $\angle 11$ and $\angle 8$ are supplementary.

  $\begin{array}{l}\text{Therefore,}m\angle 11+m\angle 8={180}^{\circ }\text{.}\hfill \\ \begin{array}{cc}m\angle 8& =180-m\angle 11\\ & =180-80\\ & =100\end{array}\hfill \end{array}$

Also it is known that sum of the measures of angles of a triangle is ${180}^{\circ }$

Therefore.

  $\begin{array}{cc}m\angle 6+m\angle 7+m\angle 8& =180\\ x+(x-20)+100& =180\\ 2x+80& =180\\ 2x& =180-80\end{array}$

Further solveing to get

  $\begin{array}{l}2x=100\\ x=50\end{array}$

Therefore, the value of $x$ is $x=50$