Chapter 12.2, Problem 33E

To determine

To find : The angles same measurement with $m\angle 1$

Answer to Problem 33E

  $m\angle 1=m\angle 3=m\angle 4=m\angle 7$

Explanation of Solution

Given information : One of the angle of the parallel line and its transversal is ${120}^{\circ }$ .

Concept used : In the parallel line and its transversal corresponding angles are equal, vertically opposite angles are equal and also alternate exterior angles are equal.

In the diagram,

  $m\angle 1=m\angle 3$ (Vertically opposite angles)

  $m\angle 1=m\angle 4$ (Corresponding angles)

  $m\angle 1=m\angle 7$ (Alternate exterior angles)

Thus, $m\angle 1=m\angle 3=m\angle 4=m\angle 7$