Question Video: Finding the Measure of an Angle given Its Supplementary Angle’s Measure Mathematics

Video Transcript

In the figure, the ray from 𝐵 through 𝐷 bisects the angle 𝐴𝐵𝐸. What is the measure of angle 𝐴𝐵𝐷?

In this question we are given a figure and asked to determine the measure of a given angle using a bisector and a given angle measure.

To answer this question, we can begin by recalling that an angle bisector bisects an angle into two angles with equal measure. In this case, we are told that the ray from 𝐵 through 𝐷 bisects angle 𝐴𝐵𝐸. So we must have that the measure of angle 𝐷𝐵𝐸 is equal to the measure of angle 𝐴𝐵𝐷. We can add this information onto the figure.

We can then recall that the measure of a straight angle is 180 degrees. And we can see in the figure that angle 𝐴𝐵𝐶 is a straight angle. Hence, the sum of the angle measures that make the straight angle is 180 degrees. We have that 180 degrees is equal to 54 degrees plus the measure of angle 𝐷𝐵𝐸 plus the measure of angle 𝐴𝐵𝐷.

Since the measure of angle 𝐷𝐵𝐸 is equal to the measure of angle 𝐴𝐵𝐷, we can replace its measure with that of the measure of angle 𝐴𝐵𝐷 to obtain two times the measure of angle 𝐴𝐵𝐷. We can then subtract 54 degrees from both sides of the equation and evaluate to get that 126 degrees is equal to the two times the measure of angle 𝐴𝐵𝐷. Finally, we can divide both sides of the equation by two to find that the measure of angle 𝐴𝐵𝐷 is 63 degrees.