First look at triangle ABC. You'll notice that it gives you that it is a 90 degree angle and that AC = BC. Because Line segments AC and BC are equal in length and are the legs of a 90 degree angle, then each of the other angles in the triangle are 45 each. (all interior angles add to 180 degrees).
Now we can look at triangle ACD. Angle a will be 120 degrees minus the 45 degree angle we found in the other triangle. So angle A = 120-45 = 75 degrees.
Now we can find angle z by adding the 2 angles we know and subtracting from 180...
75 + 90 = 165
z = 180 - 165 = 15 degrees
