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Suppose ππΈ bisects angle π΄ππ·.
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Find the measure of angle πΈππΆ.
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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.
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So weβre given the 45 degrees, the measure of angle πΆππ΅.
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And if itβs 45 degrees, angle π΄ππ· is 45 degrees.
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This is because they are vertical angles, and vertical angles are congruent.
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So if ππΈ bisected that 45-degree angle, it cut 45 degrees in half.
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So angle π΄ππΈ would be 22.5 degrees and angle πΈππ· would be 22.5 degrees.
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So this is helpful because now we know this portion of the angle that weβre looking for; πΈπC is 22.5 degrees.
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So now we need to find this remaining portion.
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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.
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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.
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And adding these together, we would get 157.5 degrees, so that would be the measure of angle πΈππΆ.