Well if you notice, 48, x, and x are all on the same line, so they must add up to equal 180 degrees. So...
2x + 48 = 180
2x = 132
x = 66
So each x is equal to 66 degrees. Now we know the triangle is a right triangle, and the sum of all interior angles must be equal to 180 degrees for a triangle. So...
66 + 90 + z = 180
156 + z = 180
z = 24
Z equals 24 degrees! I hope this helps!