Chapter 12.2, Problem 14E

To determine

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

Answer to Problem 14E

Therefore, the measurement of the angles are $m\angle 2={137}^{\circ }$ , $m\angle 3={137}^{\circ }$ , $m\angle 4={43}^{\circ }$ , $m\angle 5={43}^{\circ }$ , $m\angle 6={137}^{\circ }$ , $m\angle 7={137}^{\circ }$ , $m\angle 8={43}^{\circ }$

Explanation of Solution

Given information : $m\angle 1={43}^{\circ }$

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 :

  $\begin{array}{l}m\angle 1+m\angle 3={180}^{\circ }\\ m\angle 3={180}^{\circ }-m\angle 1\\ m\angle 3={180}^{\circ }-{43}^{\circ }{}^{}\\ m\angle 3={137}^{\circ }\end{array}$

  $m\angle 2=m\angle 3={137}^{\circ }$ (Vertically opposite angle)

  $m\angle 1=m\angle 4={43}^{\circ }$ (Vertically opposite angle)

  $m\angle 1=m\angle 5={43}^{\circ }$ (Corresponding angles)

  $m\angle 2=m\angle 6={137}^{\circ }$ (Corresponding angles)

  $m\angle 6=m\angle 7={137}^{\circ }$ (Vertically opposite angle)

  $m\angle 5=m\angle 8={43}^{\circ }$ (Vertically opposite angle)

Therefore, the measurement of the angles are $m\angle 2={137}^{\circ }$ , $m\angle 3={137}^{\circ }$ , $m\angle 4={43}^{\circ }$ , $m\angle 5={43}^{\circ }$ , $m\angle 6={137}^{\circ }$ , $m\angle 7={137}^{\circ }$ , $m\angle 8={43}^{\circ }$