Chapter 12, Problem 17CR

To determine

To find: $m\angle 7$

Answer to Problem 17CR

The measurement of $m\angle 7={65}^{\circ }$ .

Explanation of Solution

Given information : Line $m$ and $n$ are parallel, and $m\angle 1={115}^{\circ }$ .

Concept used : We know that the sum of linear pair angles is ${180}^{\circ }$ . And alternate exterior angles are always same.

Calculation :

$\angle 1$ and $\angle 2$ are linear pair angles.

  $\begin{array}{l}m\angle 1+m\angle 2={180}^{\circ }\\ \Rightarrow {115}^{\circ }+m\angle 2={180}^{\circ }\\ \Rightarrow m\angle 2={180}^{\circ }-{115}^{\circ }\\ \Rightarrow m\angle 2={65}^{\circ }\end{array}$

And, $\angle 2$ and $\angle 7$ are alternate exterior angles.

So, $m\angle 2=m\angle 7={65}^{\circ }$

Thus, the measurement of $m\angle 7={65}^{\circ }$ .