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
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.