DS

[GmatKiss]

DS

[Anurag@Gurome]

DS

BC = BD implies that BCD is an isosceles triangle.
So, angle BDC = angle BCD = xº
Angle CBD = 180 - (x + x) = 180 - 2x [Angle sum of a triangle = 180º]
So, angle ABD = 180 - (180 - 2x) = 2x [ABC is a straight line]
angle DAB = angle DBA = 2xº, which implies that triangle ABD is also isosceles


(1) x = 30 or angle BCD implies angle BDC = 30º (as BCD is isosceles triangle)
But we cannot find the length of BC from this info; NOT sufficient.

(2) AD = 1
Since angle DAB = angle DBA = 2xº, so the sides AD = BD = 1
Also since angle BDC = angle BCD = xº, so BC = BD = 1; SUFFICIENT.

The correct answer is B.