Hello from MrBillDoesMath!
Answer: a 39 degrees
Discussion:
In triangle WZY:
angle 3 + angle 5 + 138 = 180 (a triangle contains 180 degrees)
Since triangle WZY is isosceles , angle 5 = angle 3 so
angle 3 + angle 3 + 138 = 180 =>
2* (angle 3) = 180 - 138 = 42 =>
angle 3= 21 degrees
Now, triangle XWY is equilateral so each base angle is 60 degrees. But angle 2 + angle 3 is a base angle so
angle 2+ angle 3 = 60.
As angle 3 = 21 degrees (from above)
angle 2 + 21 = 60 =>
angle 2 = 60 -21 = 39 degrees
Thank you,
MrB