SOLUTION: In the figure p || q. Find m<1. Figure: imgur.com/SWBzyAw.png

Question 1117995: In the figure p || q. Find m<1.
Figure: imgur.com/SWBzyAw.png
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

There are many ways to solve this problem; all of them I think involve drawing some auxiliary line. Following is a description of the method I like to use, using a third line through S parallel to the two given parallel lines.

Here is a diagram of the given picture, with the auxiliary line added.

We then have...

Angle ABC = 125 degrees (given)
Angle CBD = 55 degrees (supplementary angles)
Angle BDE = 55 degrees (alternate interior angles)
Angle DFH = angle EDF (alternate interior angles)
Angle BDE + angle EDF = 119 degrees (given)
Angle GFI = angle DFH = angle EDF = 119 degrees - angle BDE = 119 degrees - 55 degrees = 64 degrees

Answer: The measure of angle GFI (angle 1 in your diagram) is 64 degrees
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