Geometry with Algebraic equation

I try different ways to do this but the answer I get is different than the book answer.
The book answer is 15 degrees. Can someone tell me what I am doing wrong? Thanks.

4x+55 =
    -55  = -55
       4x = -55
   4x/4 = -55/4
         x = 13.75 deg.

10x-85 =
    +85  = +85
      10x = 85
 10x/10 = 85/10
          x = 8.5 deg.

4x+55 = 10x-85
    +85 =      +85
4x+85 = 10x
-4x          -4x
      85 = 6x
   85/6 = 6x/6
   deg. 14.2 = x

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You will notice that <1 and <3 are complementary (opposite sides) given that l and m are parallel, so they ADD up to 180.

So putting all the information together

4x + 55 + 10x - 85 = 180 (degrees)

Solve that easily to get x

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kadinAuthor Commented:
Thanks a bunch. I knew the two angles added up to 180, but I did not think to add the two equations together.
You have ANGLE_P = 4x+55  and   ANGLE_Q = 10x-85
>>     4x+55 = 10x-85
So you are saying that ANGLE_P = ANGLE_Q

This would be a true statement if, for example, ANGLE_P were <1 and ANGLE_Q were <4 (since alternate interior angles are equal).
>> but I did not think to add the two equations together.

You should set up symbols, and then state what you know. For example:
ANGLE_P + ANGLE_Q = 180 (if ANGLE_P were <1  and   ANGLE_Q were <3)

Then you just plug in and solve.
kadinAuthor Commented:
That's a good idea. Thanks for that.
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