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In the figure, line m is parallel to line n. 

1) Find m

2) Name the postulates and/or theorems you used in finding your answer to Part 1. Explain each postulate or theorem. 

 

Guest Jan 8, 2018
edited by Guest  Jan 8, 2018
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7+0 Answers

 #1
avatar+86649 
+2

I think we want to find x, not m

 

Angle CDG  =  Angle JDE    { vertical angles}

Angle JDE  =  Angle HCD    {corresponding angles }

Thus

Angle CDG  = Angle HCD   { substitution }

 

So

 

5x  -  5   =   3x  +   13       add 5 to both sides, subtract 3x from both sides

 

2x   =  18            divide both sides by 2

 

x  =  9

 

 

cool cool cool

CPhill  Jan 8, 2018
 #2
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Oh! I'm sorry, I meant to put m

Guest Jan 8, 2018
 #3
avatar+7056 
0

You meant to put  m  or you meant to put  x  ?  smiley

hectictar  Jan 8, 2018
 #4
avatar
0

M should be m < BCH

Guest Jan 9, 2018
edited by Guest  Jan 9, 2018
 #5
avatar+7056 
+1

Notice that  ∠BCH  and  ∠HCD  form a straight line, so they must add to  180° .

 

∠BCH  +  ∠HCD   =   180°

 

And...

 

m∠HCD  =  (3x + 13)°        CPhill already found that  x = 9 , so that means

 

m∠HCD  =  (3(9) + 13)°

 

m∠HCD  =  (27 + 13)°

 

m∠HCD  =  40°

 

So.....remember...

 

∠BCH  +  ∠HCD   =   180°

 

∠BCH  +     40°     =   180°

 

Can you finish it from here?  smiley

hectictar  Jan 9, 2018
 #6
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+2

BCH would be 140? :) I imagine you find that by subtracting 40 from both sides, so 180 - 40 = 140

Guest Jan 9, 2018
 #7
avatar+1965 
+2

Precisely!

TheXSquaredFactor  Jan 9, 2018

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