Question 176604
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