Glencoe Math: Course 3, Volume 2
GM
Glencoe Math: Course 3, Volume 2 View details
1. Lines
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Exercise 16 Page 377

Use the relationships of angles between parallel lines.

See solution.

Practice makes perfect

We are given the following diagram.

The diagram

In this diagram, a line intersects the parallel lines and 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 is Therefore, we can use these relationships to find and Let's start by finding

The alternate exterior angles
Notice that and are exterior angles that lie on opposite sides of the transversal. This means that and are alternate exterior angles. Since and are parallel, the measures of these angles are equal.
Next, we will find the measure of To do so, let's take a closer look at and
The supplementary angles
We can see that and form a straight line, which means that and are supplementary. The measures of supplementary angles always add up to
Since we know that we can find the measure of
We found that and