The angles that are 105º and (13x + 66)º are the same amount.
105 = 13x + 66
Subtract 66 from each side
39 = 13x
Divide each side by 13
3 = x
Now for z.
Since two equal angles equal 105º each, multiply it by 2 to get 210.
The whole thing is 360º.
360 - 210 = 50
Divide it by 2 to get one of the angles
50 / 2 = 25
z = 25º
Hope this helps!