October 27th, 2017, 05:46 PM  #1 
Senior Member Joined: Jan 2017 From: US Posts: 120 Thanks: 6  Construct a TwoColumn Proof
Hello, Can anyone help me with this question? Given that m ∠2 = (4x + 20)° and m ∠3 = (x − 10)°, prove that m ∠2 = 156° by constructing a twocolumn proof. You must include a twocolumn proof with a column for statements and a column for reasons that justify your statements. 
October 27th, 2017, 06:04 PM  #2 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,958 Thanks: 1146 Math Focus: Elementary mathematics and beyond 
Sure, we can help. What have you done to solve this so far? Where are you having difficulty?

October 27th, 2017, 06:14 PM  #3 
Senior Member Joined: Jan 2017 From: US Posts: 120 Thanks: 6 
I'm having difficulty with the whole "proving it" thing.

October 27th, 2017, 06:22 PM  #4 
Senior Member Joined: Jan 2017 From: US Posts: 120 Thanks: 6 
This is about as far as I've gotten. Sooo if anyone has any advice they'd like to offer, it'd be appreciated.

October 27th, 2017, 06:25 PM  #5 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,958 Thanks: 1146 Math Focus: Elementary mathematics and beyond 
Statement: (4x + 20)$^\circ$ + (x  10)$^\circ$ = 180$^\circ$ Reason: the sum of adjacent angles on a straight line is 180$^\circ$ Can you continue? (You might have a different way of stating what I said above in the "Reason") 
October 27th, 2017, 06:35 PM  #6 
Senior Member Joined: Jan 2017 From: US Posts: 120 Thanks: 6  So then the answer to that would be 5x + 10? So could you find x by doing (4x+20)= 156, since angle 2 is 156 degrees?

October 27th, 2017, 06:42 PM  #7 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,958 Thanks: 1146 Math Focus: Elementary mathematics and beyond 
You're trying to prove angle 2 is 156 degrees, so you can't use that. You are not trying to find x, though you have to do that as an intermediate step. If you have 4x + 20 + x  10 = 180, what is x? 
October 27th, 2017, 07:00 PM  #8  
Senior Member Joined: Jan 2017 From: US Posts: 120 Thanks: 6  Quote:
(4(34)+20) + (3410) is 180. So then that proves it, right? Because it proves the first part of the statement is 156? Last edited by skipjack; October 27th, 2017 at 08:49 PM.  
October 27th, 2017, 07:07 PM  #9 
Senior Member Joined: Jan 2017 From: US Posts: 120 Thanks: 6 
Ok, I got it. Thanks!

October 27th, 2017, 08:53 PM  #10 
Global Moderator Joined: Dec 2006 Posts: 20,924 Thanks: 2203 
That's mathematically correct, but your calculations (that x = 34, etc.) presumably should be done in detail in twocolumn format.


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