But here, the slope of the line is irrelevant. what is our concern are the angle the line formed with the two parallel lines...........it is a different story

Yeah I'm just asking as a general matter, trying to understand what we can and cannot assume from figures on the GRE. I know they say you can't assume anything, but how far does that extend?

The acute and obtuse angles formed out of a transversal are equal

So \(x=z\)

Now \(z+y=180^\circ\)

Quantity A = \(y-z\)
Quantity B = \(x\)

If \(y=110^\circ\) and \(z=70^\circ\), \(y-z=40^\circ\) and thus \(y-z<x\)

If \(y=120^\circ\) and \(z=60^\circ\), \(y-z=60^\circ\) and thus \(y-z=x\)

If \(y=130^\circ\) and \(z=50^\circ\), \(y-z=80^\circ\) and thus \(y-z>x\)

Thus no relationship exists between Quantity A and Quantity B

The answer is D