X and Y are the opposite given angles:
X = 45, Y = 30
Now look at the triangle made from A P and Z
Angle A = y = 30, Angle P = 30
The three inside angles of a triangle need to equal 180 degree, so Angle Z = 180 -30 - 30 = 120 degrees.
Z and W are vertical angles, which mean they are equal, so X also equals 120 degrees.
W = 120
X = 45
Y = 30
