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October 29th, 2017, 06:29 PM   #1
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Prove x=22

I have another "construct a 2-column proof" question:

Given that m ∠4 = (5x − 2)° and m ∠3 = 72°, prove x=22.

I have to create a two column proof, with one column for statements and one column for reasons.

However, wouldn't angle 3 and angle 4 be supplementary? If not what kind of angles are they? If I can calculate the measure of angle 4 by knowing how it's related to angle 3, I can probably do the 2 column proof.

Any help will be appreciated!
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October 29th, 2017, 06:41 PM   #2
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The angles 3 and 4 are supplementary.
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October 31st, 2017, 09:20 AM   #3
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Yes, angles 3 and 4 are supplementary. That means that 5x - 2 + 72 = what?

Last edited by skipjack; November 17th, 2017 at 09:19 PM.
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November 17th, 2017, 04:26 PM   #4
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"Two column proof'


STATEMENTS REASONS
m angle 4= 5x- 2 degrees Given
m angle 3= 72 degrees Given
(5x- 2)+ 72= 180 Adjacent angles making a straight line are supplementary
5x+ 70= 180 Addition
5x= 180- 70= 110 Subtract 70 from both sides
x= 110/5= 22 Divide both sides by 5
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November 17th, 2017, 05:09 PM   #5
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My tenth grade geometry teacher told us: s for straight: supplementary. c for corner: complementary. Just a fond memory. I had a great teacher for that class.
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November 17th, 2017, 09:56 PM   #6
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One could be more detailed.

m$\small\angle$4 = (5x − 2)° and m$\small\angle$3 = 72° (given).
The lines that appear straight in the diagram are straight (assumption).
Let 5 denote the angle comprising angles 3 and 4 (definition).
m$\small\angle$5 = 180° (definition of straight angle).
m$\small\angle$3 + m$\small\angle$4 = m$\small\angle$5 (angle addition postulate).
72° + (5x − 2)° = 180° (substitution property of equality).
etc.
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