October 29th, 2017, 06:29 PM  #1 
Senior Member Joined: Jan 2017 From: US Posts: 104 Thanks: 5  Prove x=22
I have another "construct a 2column 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! 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: 7,659 Thanks: 964 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: 2,874 Thanks: 766 
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: 2,874 Thanks: 766 
"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: 1,659 Thanks: 427 
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: 18,241 Thanks: 1438 
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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