Hi prernamalhotra,
Brent has already explained the "math" behind this question, so I won't rehash that here. Instead, I'll show you a quick way to figure out that the "left" triangle is isosceles: TEST VALUES....
Since the variable X shows up in both triangles, the angles will relate to one another - you just have to figure out HOW they relate.
If X = 10, then 2X = 20 and the angle "next to" 2X = 160. So, the third angle in the "left" triangle is 10; we have a 10/10/160, which is ISOSCELES.
If X = 20, then 2X = 40 and the angle "next to" 2X = 140. So, the third angle in the "left" triangle is 20; we have a 20/20/140, which is ISOSCELES.
IF X = 25, then 2X = 50 and the angle "next to" 2X = 130. So, the third angle in the "left" triangle is 25; we have a 25/25/130, which is ISOSCELES.
This proves a pattern. Whatever we pick for X, we end up with an ISOSCELES triangle.
With this information, it becomes really easy to deal with Fact 1 (you can point to all of the Isosceles triangle sides - they all equal 6) and Fact 2 (it has no information on the lengths of sides, so it can't be enough to answer the question).
You can TEST VALUES in may questions to discover patterns and get the correct answer, so keep it in mind when you see variables in a prompt.
GMAT assassins aren't born, they're made,
Rich
