Solve GRE Geometry Problem: X-Y = 30

[Spirochete]

I've attached an MS paint version of a GRE geometry problem. It's a quantitative comparison question. It asks you to compare two values and say whether one is greater, they're the same, or they're not enough information to say which is greater.

In the picture I drew everything is in degrees. It's not necessarily to scale.

As I've said in the picture, the actual answer is that (X-Y) is equal to the value 30. I have no clue how they figured this out though I would've said not enough information to answer.

 

[rock.freak667]

Notice that 2X+2Y=180 and that 2X+Y+30=180.

Two equations, two unknows, solve for X and Y, then compute X-Y.

 

[Spirochete]

Brilliant. thank you.