Data Sufficiency

how can arrive at the answer when it's not given that 2 lines are perpendicular

Hi,

Focus on the interior angles of the triangle. Let's call them A (near x), B (near Y) and C (near Z). Notice that Angles x and A total 180 degrees because they form a line. Same with B and y. And same with C and z. Also, there are 180 degrees in the triangle.

Knowing that x=y tells us that A=B. But there are many possible degrees for A and B if we don't know what angle C is. So, we are down to answer choices BCE.

Knowing that x=z tells us that A=C. Same problem, however; we would need info about angle B. So, we are down to answer choices CE.

If x=y and x=z, then A=B and A=C, which means A, B, C are equal. Because there are 180 degrees in the triangle, each of A, B and C measures 60 degrees. Thus, we have sufficient information to find x (which is 120 degrees).

So, answer (C).

It never says that the figure is a triangle, so you won't be able to figure it out.

E

Edit: Now I'm doubting myself. Since the angles are given, perhaps you can assume that the lines touch.