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Thanks a bunch. I knew the two angles added up to 180, but I did not think to add the two equations together.
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Thanks a bunch. I knew the two angles added up to 180, but I did not think to add the two equations together.

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You have ANGLE_P = 4x+55 &nbsp;and &nbsp; ANGLE_Q = 10x-85<br />
&gt;&gt;&nbsp; &nbsp; &nbsp;4x+55 = 10x-85<br />
So you are saying that ANGLE_P = ANGLE_Q<br />
<br />
This would be a true statement if, for example, ANGLE_P were &lt;1 and ANGLE_Q were &lt;4 (since alternate interior angles are equal).
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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).

<div>
&gt;&gt; but I did not think to add the two equations together.<br />
<br />
You should set up symbols, and then state what you know. For example:<br />
ANGLE_P + ANGLE_Q = 180 (if ANGLE_P were &lt;1 &nbsp;and &nbsp; ANGLE_Q were &lt;3)<br />
<br />
Then you just plug in and solve.
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>> 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.

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That's a good idea. Thanks for that. 
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<div class="content wysiwyg-content">
I try different ways to do this but the answer I get is different than the book answer.<br />
The book answer is 15 degrees. Can someone tell me what I am doing wrong? Thanks.<br />
<br />
4x+55 = <br />
&nbsp; &nbsp; -55 &nbsp;= -55<br />
&nbsp; &nbsp; &nbsp; &nbsp;4x = -55<br />
&nbsp; &nbsp;4x/4 = -55/4<br />
&nbsp; &nbsp; &nbsp; &nbsp; &nbsp;x = 13.75 deg.<br />
<br />
10x-85 = <br />
&nbsp; &nbsp; +85 &nbsp;= +85<br />
&nbsp; &nbsp; &nbsp; 10x = 85<br />
&nbsp;10x/10 = 85/10<br />
&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; x = 8.5 deg.<br />
<br />
4x+55 = 10x-85<br />
&nbsp; &nbsp; +85 = &nbsp; &nbsp; &nbsp;+85<br />
4x+85 = 10x<br />
-4x &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;-4x<br />
&nbsp; &nbsp; &nbsp; 85 = 6x<br />
&nbsp; &nbsp;85/6 = 6x/6<br />
&nbsp; &nbsp;deg. 14.2 = x<br />
<br />
<br />
<a href="https://filedb.experts-exchange.com/incoming/2011/04_w16/442944/geo01.jpg" target="_blank" class="file-inline" title="geo01 (74 KB)"><svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512"><path d="M67.508 468.467c-58.005-58.013-58.016-151.92 0-209.943l225.011-225.04c44.643-44.645 117.279-44.645 161.92 0 44.743 44.749 44.753 117.186 0 161.944l-189.465 189.49c-31.41 31.413-82.518 31.412-113.926.001-31.479-31.482-31.49-82.453 0-113.944L311.51 110.491c4.687-4.687 12.286-4.687 16.972 0l16.967 16.971c4.685 4.686 4.685 12.283 0 16.969L184.983 304.917c-12.724 12.724-12.73 33.328 0 46.058 12.696 12.697 33.356 12.699 46.054-.001l189.465-189.489c25.987-25.989 25.994-68.06.001-94.056-25.931-25.934-68.119-25.932-94.049 0l-225.01 225.039c-39.249 39.252-39.258 102.795-.001 142.057 39.285 39.29 102.885 39.287 142.162-.028A739446.174 739446.174 0 0 1 439.497 238.49c4.686-4.687 12.282-4.684 16.969.004l16.967 16.971c4.685 4.686 4.689 12.279.004 16.965a755654.128 755654.128 0 0 0-195.881 195.996c-58.034 58.092-152.004 58.093-210.048.041z"/></svg>geo01.jpg</a>
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geo01.jpg

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



Geometry with Algebraic equation

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