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October 29th, 2017, 05:29 PM   #1
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Joined: Jan 2017
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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!
Attached Images geometry_question_9.jpg (9.8 KB, 4 views)

Last edited by Indigo28; October 29th, 2017 at 05:30 PM. Reason: To add a picture October 29th, 2017, 05:41 PM #2 Global Moderator   Joined: Oct 2008 From: London, Ontario, Canada - The Forest City Posts: 7,963 Thanks: 1148 Math Focus: Elementary mathematics and beyond The angles 3 and 4 are supplementary. October 31st, 2017, 08:20 AM #3 Math Team   Joined: Jan 2015 From: Alabama Posts: 3,264 Thanks: 902 Yes, angles 3 and 4 are supplementary. That means that 5x - 2 + 72 = what? Last edited by skipjack; November 17th, 2017 at 08:19 PM. November 17th, 2017, 03:26 PM #4 Math Team   Joined: Jan 2015 From: Alabama Posts: 3,264 Thanks: 902 "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, 04:09 PM #5 Senior Member   Joined: Aug 2012 Posts: 2,393 Thanks: 749 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, 08:56 PM #6 Global Moderator   Joined: Dec 2006 Posts: 20,970 Thanks: 2222 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. Tags prove, x22 Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post boo Applied Math 3 January 4th, 2015 12:52 AM kaspis245 Algebra 3 November 9th, 2014 07:47 AM octaveous Number Theory 13 September 23rd, 2010 04:36 AM qweiop90 Algebra 1 July 31st, 2008 06:27 AM qweiop90 New Users 1 December 31st, 1969 04:00 PM

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