SOLUTION: This question has an image on it, so I can't write it down... I put an image of it online. http://i42.tinypic.com/2qd90z7.jpg Thank you very much!

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Let's call the vertex where the rays originate V.
Then angle 1 would also be angle WVK.
The supplementary angles are 120 degrees and angle J (or angle KVZ), they sum to 180 degrees.
The vertical angles would be angle J (angle KVZ) and angle XVY.
From the diagram,
Angle 1 + 55 = 120
Angle 1 = 120-55
Angle 1=65

You can put this solution on YOUR website!
Remember:
Supplementary angles are two angles with a of .
Vertical angles are two angles whose sides form two pairs of . We can think of these as opposite angles by an .
I assume is a point where lines cross.
So, supplementary angles are:
< and <,
< and <,
< and <,
< and <

Vertical angles are:
< is vertical with <,
< is vertical with <,

In each case these pairs of angles form an .