Chapter 4, Problem 11CUR

To determine

Find the measure of each numbered angle.

Answer to Problem 11CUR

  $m\angle 5=90°$

  $m\angle 6=54°$

  $m\angle 7=36°$

  $m\angle 8=54°$

Explanation of Solution

Given:

  

Calculation:

The diagram is :

  

Since $AB\parallel CD$

  $m\angle 5=m\angle F=90°$ , since they are corresponding angles , where FE is the transversal and AB is parallel to CD.

  $\begin{array}{l}m\angle 5+m\angle 6+m\angle GEC=180°\mathrm{................}[\text{linear angles]}\\ \Rightarrow m\angle 6+90°+36°=180°\\ \Rightarrow m\angle 6=180°-126°\mathrm{.................}[\text{subtract 126}°\text{ from each side]}\\ \Rightarrow m\angle 6=54°\end{array}$

  $m\angle 7=m\angle 6=36°$ , since they are vertically opposite angles , where GE is the transversal and AB is parallel to CD.

  $m\angle 8=m\angle GEC=54°$ , since they are vertically opposite angles , where GE is the transversal and AB is parallel to CD.

So,

  $m\angle 5=90°$

  $m\angle 6=54°$

  $m\angle 7=36°$

  $m\angle 8=54°$