Exercise 16 Page 377

We are given the following diagram.

In this diagram, a line intersects the parallel lines $a$ and $b.$ When two parallel lines are cut by a transversal, special angle relationships exist. If we know the measure of one of the angles, we can find the measures of all of the angles. In this case, we know that $m\angle 1$ is $120^{\circ }.$ Therefore, we can use these relationships to find $m\angle 2$ and $m\angle 3.$ Let's start by finding $m\angle 2.$

Notice that $\angle 1$ and $\angle 2$ are exterior angles that lie on opposite sides of the transversal. This means that $\angle 1$ and $\angle 2$ are alternate exterior angles. Since $a$ and $b$ are parallel, the measures of these angles are equal. Next, we will find the measure of $\angle 3.$ To do so, let's take a closer look at $\angle 2$ and $\angle 3.$ We can see that $\angle 2$ and $\angle 3$ form a straight line, which means that $\angle 2$ and $\angle 3$ are supplementary. The measures of supplementary angles always add up to $180^{\circ }.$ Since we know that $m\angle 2=120^{\circ },$ we can find the measure of $\angle 3.$ We found that $m\angle 2=120^{\circ }$ and $m\angle 3=60^{\circ }.$