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.
