What is the measurement of angle h?

To find the other angle, we can see that 148 is supplementary to 32. 

Since the total angle in a triangle is 180, we can find h:
h = 180 - 32 - 56 = 92^o

Because we know that the sum of all 3 angles of a triangle is 180, and angle of a striaght line is 180, we know that the missing angle that is not h is 180-148=32, and because the sum of the 3 angles inside a triangle is 180, we know that 32+56+h=180, and simplifying, we have $h=92^\circ$