Chapter 12.2, Problem 15E

a.

To determine

To identify: the type of angles $\angle 1$ and $\angle 2$

Answer to Problem 15E

The angles are alternate interior angles.

Explanation of Solution

Concept used : Two angles that lie between the two parallel lines on opposite side of the transversal line is known as alternate interior angles.

Here, $\angle 1$ and $\angle 2$ lie between the two parallel lines on opposite side of the transversal line.

b.

To determine

Do $\angle 1$ and $\angle 2$ have the same measure?

Answer to Problem 15E

Yes, $\angle 1$ and $\angle 2$ have the same measure.

Explanation of Solution

Given information: $m$ and $n$ parallel line and $t$ is the transversal line.

Concept Used: Two angles that lie between the two parallel lines on opposite side of the transversal line is known as alternate interior angles.

Here, $\angle 1$ and $\angle 2$ lie between the two parallel lines on opposite side of the transversal line.

c.

To determine

To calculate: the value of angles $\angle 1$ and $\angle 2$

Answer to Problem 15E

Therefore, $m\angle 1={72}^{\circ }$ and $m\angle 2={72}^{\circ }$

Explanation of Solution

Given information: $m$ and $n$ parallel line and $t$ is the transversal line and one of its angle is ${108}^{\circ }$

Concept used : Sum of linear pair angles are ${180}^{\circ }$ . Alternate interior angles are always equal.

Calculation:

According to the problem,

  $\begin{array}{l}m\angle 2+{108}^{\circ }={180}^{\circ }\\ \Rightarrow m\angle 2={180}^{\circ }-{108}^{\circ }\\ \Rightarrow m\angle 2={72}^{\circ }\end{array}$

  $m\angle 1=m\angle 2$ (Alternate interior angles)

So, $m\angle 1=m\angle 2={72}^{\circ }$