OG quant DS geometry - ?Mistake

Well that's what I thought but here's what the solution says:

Answer = A

Solution:
The degreee measure of an exterior angle of a triangle is equal to the sum of the remote interior angles. Note that angle BDC (with an angle measure of 2x) is an exterior angle of triangle ADB and has an angle measure equal to the sum of the remote interior angles ABD and DAB. Thus, if the angle ABD has measure y degrees, then x+y = 2x, or when simplified, y = x. Since two angles of triangle ABD are equal, then the sides opposite these angles have the same length and AD=DB. For the same reason DB=BC. If AD = DB and DB = BC, then AD = BC.

1) If AD = 6, then BC must also equal 6;
SUFFICIENT

?????? Can anyone help????????

I dont understand how it gets x+y = 2x?

I understand the whole remote interior angle rule but isn't that just saying that the sum of angles ABD + DAB = 2x. It seems that it is then assuming that angles ABD and DAB are equal!?!?

From the information we're given we dont know that AD = BD

There's a typo in the book. I know this for a fact.

Can anyone tell me what the OG quant book is?
Thanks

GMAT Officiant Guide Quantitative Review