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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. Jan 8, 2018
edited by Guest  Jan 8, 2018

#1
+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   Jan 8, 2018
#2
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Oh! I'm sorry, I meant to put m

Guest Jan 8, 2018
#3
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You meant to put  m  or you meant to put  x  ? hectictar  Jan 8, 2018
#4
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M should be m < BCH

Guest Jan 9, 2018
edited by Guest  Jan 9, 2018
#5
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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? hectictar  Jan 9, 2018
#6
+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
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Precisely!

TheXSquaredFactor  Jan 9, 2018