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October 27th, 2017, 05:46 PM   #1
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Construct a Two-Column 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 two-column proof. You must include a two-column proof with a column for statements and a column for reasons that justify your statements.
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 October 27th, 2017, 06:04 PM #2 Global Moderator     Joined: Oct 2008 From: London, Ontario, Canada - The Forest City Posts: 7,806 Thanks: 1045 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: 109 Thanks: 5 I'm having difficulty with the whole "proving it" thing.
October 27th, 2017, 06:22 PM   #4
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This is about as far as I've gotten. Sooo if anyone has any advice they'd like to offer, it'd be appreciated.
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 October 27th, 2017, 06:25 PM #5 Global Moderator     Joined: Oct 2008 From: London, Ontario, Canada - The Forest City Posts: 7,806 Thanks: 1045 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
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Quote:
 Originally Posted by greg1313 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")
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: 7,806 Thanks: 1045 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
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Quote:
 Originally Posted by greg1313 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?
x is 34. So
(4(34)+20) + (34-10) 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: 109 Thanks: 5 Ok, I got it. Thanks!
 October 27th, 2017, 08:53 PM #10 Global Moderator   Joined: Dec 2006 Posts: 18,956 Thanks: 1602 That's mathematically correct, but your calculations (that x = 34, etc.) presumably should be done in detail in two-column format.

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