The question asks the length of side BC. From the figure, you can see that triangle BDC is an isosceles triangle with BD = BC. Thus, to know the length of BC, it is okay if we know the length of BD.
To solve such problems, you have to know that in a triangle, the measure of the exterior angle is equal to the sum of the two non-adjacent angles of the triangle.
That is, in the given figure, for triangle ABD, angle BDC is the exterior angle. Thus, BDC = ABD + BAD
That is, 2x = ABD + x. Thus ABD = x.
Now, you can see that triangle ABD is an isosceles triangle in which AD = BD = 6. Thus, BD = BC = 6. SUFFICIENT
x = 36 does not tell you anything about the length of any side. INSUFFICIENTAnswer: A
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