Data Sufficiency

So once agian, the correct answer is A, I put E

How is it A? You only know AD which is 6, how does that give you the length of BC? I mean the triangle that BC is in is an isoceles, or equliateral (not sure), but still.....

Got this one wrong myself. Here's what I learned:

Angle BDC = 2x is an exterior angle of triangle ABD.

Hence, it is the sum of the two non-adjacent angles. This is the key rule I didn't know beforehand. You can plug in numbers to find out that this will always be true.

That is: angle BDC = angle BAD + angle ABD
Hence: 2x = x + angle ABD
Then: angle ABD = x

Once you know this, you know AD = BD because it's an isosceles triangle, and likewise for BD = BC. Thus, AD = BD = BC.

So (1) is sufficient.