Question Video: Finding the Measure of an Angle given Its Corresponding Angle’s Measure Mathematics • 8th Grade

Video Transcript

In the figure below, find the measure of angle 𝐴𝐵𝐶.

The first thing we might notice in this question is that we have two parallel line segments, 𝐴𝐷 and 𝐵𝐶. The line segment 𝐵𝐸 forms a transversal of these two parallel line segments. And we should recall that there are some special angle properties when we have an arrangement of two parallel lines and a transversal.

We can, for example, have corresponding angles, alternate interior angles, and alternate exterior angles. In each case, these angles will all be equal in measure. We also have the property that the interior angles on the same side of the transversal are supplementary, which means they add to 180 degrees. So let’s consider if we have any of these angle arrangements in the original figure.

We are given this angle measure of 𝐸𝐴𝐷 as 65 degrees. And we can identify that we have a corresponding angle at angle 𝐴𝐵𝐶. Corresponding angles are equal in measure. So both of these angles have a measure of 65 degrees. Therefore, the answer is that the measure of angle 𝐴𝐵𝐶 is 65 degrees.