Glencoe Math: Course 3, Volume 2
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Glencoe Math: Course 3, Volume 2 View details
1. Lines
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Exercise 21 Page 377

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. We can use these relationships to find the measure of the angle. Let's start by marking an extra angle in the diagram.

The diagram with a new angle marked

To find the the measure of we can analyze the relationship between the angle and

The corresponding angles
The angle and are in the same position on the two lines in relation to the transversal. This means that the angle and are corresponding angles. Since and are parallel, the measures of these angles are equal.
Now let's take a closer look at and the angle.
The supplementary angles
We can see that and the angle form a straight line. Therefore, and the angle are supplementary and the sum of their measures is
Since we know that we can find the value of
We found that This means that the correct option is D.