### Video Transcript

Suppose ππΈ bisects angle
π΄ππ·. Find the measure of angle
πΈππΆ.

So we are told that ππΈ bisects
angle π΄ππ·, so it cuts it in half, and we wanna know the measure of angle
πΈππΆ. So weβre given the 45 degrees, the
measure of angle πΆππ΅. And if itβs 45 degrees, angle
π΄ππ· is 45 degrees. This is because they are vertical
angles, and vertical angles are congruent.

So if ππΈ bisected that 45-degree
angle, it cut 45 degrees in half. So angle π΄ππΈ would be 22.5
degrees and angle πΈππ· would be 22.5 degrees. So this is helpful because now we
know this portion of the angle that weβre looking for; πΈπC is 22.5 degrees.

So now we need to find this
remaining portion. Well, if π΅π· is a straight line,
then it should add to 180 degrees, and we already know this much of it is 45
degrees, so the remaining will be the piece that we need.

So 180 minus 45 would give us 135
degrees, so the angle that weβre looking for, πΈππΆ, will be 135 degrees plus 22.5
degrees. And adding these together, we would
get 157.5 degrees, so that would be the measure of angle πΈππΆ.