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Angle BDC = Angle BCD implies BD = BC ( equal angles have equal sides opposite to them)
Also, exterior angle ADB = 180 - 2x
Sum of the angles of a triangle = 180 degrees
So, in triangle ADB, x + (180 - 2x) + angle ABD = 180 implies angle ABD = x
Angle ABD = x, which is equal to angle DAB
So, AD = BD implies AD = BD = BC
We have to find BC.

Statement 1: AD = 6 implies AD = BD = BC = 6; SUFFICIENT.

Statement 2: x = 36 implies we know the angles but this does not help to find the length of BC; NOT sufficient.

The correct answer is A.

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PLUG IN FOR THE ANGLES to see how they affect each other.
Just be sure to:

-- Satisfy the conditions in the problem.
-- Satisfy the rules of geometry (the sum of angles that form a straight line must be 180, etc.).



The drawings above show two combinations of angles that satisfy the rules of geometry and all of the conditions in the problem.
In each case, angle BAD = angle ABD and angle BDC = angle BCD.
Thus, AD = BD = BC.
Thus, to determine the length of BC, we need to know the length of AD or BD.

Question rephrased: What is the length of AD or BD?

Statement 1: AD = 6.
Sufficient.

Statement 2: x=36.
No information about the any of the lengths.
Insufficient.

The correct answer is A.

_________________
Mitch Hunt
GMAT Private Tutor and Instructor
GMATGuruNY@gmail.com
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