Exercise 20 Page 377

We are asked to draw a pair of parallel lines cut by a transversal. Once we do it, we should estimate the measure of one of the angles formed. Then we are going to label the other angles with their measures as well. Let's do it!

One way of estimating the measure of $\angle 1$ is by using a protractor. This is how we know that the measure of $\angle 1$ is approximately $110^{\circ }.$

Now, there are in total eight angles formed by the lines and the transversal. Let's add them onto the graph and then find their measures without using the protractor again.

In the graph there are two angles that are supplementary with angle $1\text{:}$ angles $2$ and $4.$ Since the measures of supplementary angles add up to $180^{\circ },$ the measure of angles $2$ and $4$ is $180^{\circ }-110^{\circ }={70}^{\circ }.$

Now, there are two pairs of alternate exterior angles. One pair is $\angle 1$ and $\angle 7,$ the other pair is $\angle 2$ and $\angle 8.$ We know that their angle measures are the same because the lines are parallel. Let's include this fact in the graph.

Now, angles $1$ and $3$ have the same measure because they are vertical angles.

Last, there are two pairs of alternate interior angles — $\angle 3$ and $\angle 5,$ and also $\angle 4$ and $\angle 6.$ Once again, their measures are the same because the lines are parallel.

We successfully estimated the measure of all angles in the graph.