My Math Forum Prove x=22

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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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Last edited by Indigo28; October 29th, 2017 at 06:30 PM. Reason: To add a picture

 October 29th, 2017, 06:41 PM #2 Global Moderator     Joined: Oct 2008 From: London, Ontario, Canada - The Forest City Posts: 7,726 Thanks: 988 Math Focus: Elementary mathematics and beyond The angles 3 and 4 are supplementary.
 October 31st, 2017, 09:20 AM #3 Math Team   Joined: Jan 2015 From: Alabama Posts: 2,944 Thanks: 797 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.
 November 17th, 2017, 04:26 PM #4 Math Team   Joined: Jan 2015 From: Alabama Posts: 2,944 Thanks: 797 "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
 November 17th, 2017, 05:09 PM #5 Senior Member   Joined: Aug 2012 Posts: 1,703 Thanks: 451 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.
 November 17th, 2017, 09:56 PM #6 Global Moderator   Joined: Dec 2006 Posts: 18,559 Thanks: 1481 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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