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 20 Page 377

First, try finding two angles that are supplementary with the angle you labeled.

Practice makes perfect

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!

parallel lines cut by a transversal

One way of estimating the measure of is by using a protractor. This is how we know that the measure of is approximately

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 angles and Since the measures of supplementary angles add up to the measure of angles and is

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

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

Last, there are two pairs of alternate interior angles and and also and Once again, their measures are the same because the lines are parallel.

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