Chapter 12.2, Problem 7E

To determine

To calculate the value of angle: $\angle 2$ , $\angle 3$ , $\angle 4$ , $\angle 5$ , $\angle 6$ , $\angle 7$ and $\angle 8$

Answer to Problem 7E

Therefore, the measurement of the angles are $m\angle 2={115}^{\circ }$ , $m\angle 3={115}^{\circ }$ , $m\angle 4={65}^{\circ }$ , $m\angle 5={65}^{\circ }$ , $m\angle 6={115}^{\circ }$ , $m\angle 7={115}^{\circ }$ , $m\angle 8={65}^{\circ }$

Explanation of Solution

Given information : $m\angle 1={65}^{\circ }$

Concept used : If transversal line intersects a parallel line, corresponding angles are equal.

The values of vertically opposite angle are equal. The sum of linear pair angles are ${180}^{\circ }$ .

Calculation :

  $\begin{array}{l}m\angle 1+m\angle 3={180}^{\circ }\\ m\angle 3={180}^{\circ }-m\angle 1\\ m\angle 3={180}^{\circ }-{65}^{\circ }{}^{}\\ m\angle 3={115}^{\circ }\end{array}$

  $\angle 3$ and $\angle 2$ are vertically opposite angle.

  $m\angle 2=m\angle 3={115}^{\circ }$

  $\angle 1$ and $\angle 4$ are vertically opposite angle.

  $m\angle 4=m\angle 1={65}^{\circ }$

  $m\angle 5={65}^{\circ }$ , because $\angle 5$ and $\angle 1$ are corresponding angles.

  $m\angle 6=m\angle 2={115}^{\circ }$ because $\angle 6$ and $\angle 2$ are corresponding angles.

  $m\angle 7=m\angle 3={115}^{\circ }$ because $\angle 7$ and $\angle 3$ are corresponding angles.

  $m\angle 8=m\angle 4={65}^{\circ }$ because $\angle 8$ and $\angle 4$ are corresponding angles.

Therefore, the measurement of the angles are $m\angle 2={115}^{\circ }$ , $m\angle 3={115}^{\circ }$ , $m\angle 4={65}^{\circ }$ , $m\angle 5={65}^{\circ }$ , $m\angle 6={115}^{\circ }$ , $m\angle 7={115}^{\circ }$ , $m\angle 8={65}^{\circ }$