Chapter 3, Problem 5CR

To determine

To complete: the blank in the given statement.

Explanation of Solution

Given information:

The given figure is as follows

The given statement is “If $m\angle 1=105$ , then $m\angle 5=$

  $\underset{\_}{}$ and $m\angle 7=$

  $\underset{\_}{}$ ”

When a transversal crosses the two parallel lines, the alternate exterior angles are equal.

The angles $\angle 1\approx \angle 7$

And also definition of supplementary angles

  $\begin{array}{l}\angle 5={180}^0-\angle 6\\ ={180}^0-{180}^0+\angle 7\\ ={105}^0\end{array}$

Hence,

The blank is filled with term $m\angle 5=$

  $\underset{\_}{\text{ 105 }}$ and $m\angle 7=$

  $\underset{\_}{\text{ 105 }}$ .