# Video: Finding the Measure of an Angle Given Its Supplementary Angleβs Measure

Suppose ππΈ bisects β π΄ππ·, find πβ πΈππΆ.

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### Video Transcript

Suppose ππΈ bisects angle π΄ππ·. Find the measure of angle πΈππΆ.

So we are told that ππΈ bisects angle π΄ππ·, so it cuts it in half, and we wanna know the measure of angle πΈππΆ. So weβre given the 45 degrees, the measure of angle πΆππ΅. And if itβs 45 degrees, angle π΄ππ· is 45 degrees. This is because they are vertical angles, and vertical angles are congruent.

So if ππΈ bisected that 45-degree angle, it cut 45 degrees in half. So angle π΄ππΈ would be 22.5 degrees and angle πΈππ· would be 22.5 degrees. So this is helpful because now we know this portion of the angle that weβre looking for; πΈπC 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 weβre looking for, πΈππΆ, 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 πΈππΆ.