If KL is parallel to MN, Is x> y?

Imagine to start that NK and ML are perpendicular to the parallel lines. That would mean that they are also the same length. Bending the angles of either line in either direction would then cause the length of that line to increase by a proportional amount since the line would have to stretch to reach the other end. Therefore, simply by knowing the relative lengths of the lines we can deduce information about the relative size of the angles.

1) This tells us that we "bent" KN further than LM however we don't know in which direction. Therefore we don't know if angle x is getting bigger or smaller.
-----> INSUFFICIENT

2) This tell us NK was "bent" to the right while ML was bent to the "left" but we have no idea by how much
------> INSUFFICIENT

1&2) This tell us NK was "bent" to the right while ML was bent to the "left" + NK bended more than ML. Therefore x>y.
-----> SUFFICIENT

Answer: C