Official explanation by Manhattan GRE:
Because n is a straight line, the 4 angles above line n must add up to 180 degrees:
x + 3y = 180
We are also told that x + y = 80. The easiest method for solving these two equations involving two unknowns x and y is to simply subtract the second equation from the first, eliminating x in the process:
Therefore y = 50. Next, using x + y = 80 we obtain x = 30. Finally, noting that angles x and z together constitute the “underside” of straight line m, we can write:
x + z = 180.
This leads us to z = 150. The final answer to the question is given by:
z – y = 150 – 50 = 100.
Of course, we could also have observed that the angle with measure z degrees is opposite the totality of the 3 angles with measure y degrees each, such that z = 3 y . This would have made it unnecessary to solve for x as an intermediate step. Furthermore, knowing z = 3 y we could then write:
z – y = 3y – y = 2y.
Thus we could obtain the answer directly as 2y = 100, as derived above.
The correct answer is 100.