Consider triangle ABCMjkourtis wrote:See attachment for the figure.
What is BC?
(i) AD= 6
(ii) x=36
angle(B) = 180 - angle(A) - angle(C)
=> angle(B) = 180 - x - 2x = 180 - 3x
and angle(B) = angle(b1) + angle(b2)
Now, consider triangle DBC
angle(b1) = 180 - angle(d) - angle(C)
angle(b1) = 180 -2x -2x = 180 - 4x
angle(B) = angle(b1) + angle(b2)
180 - 3x = 180 - 4x + angle(b2)
=>angle(b2) = x
So, angle(A) = angle(b2) = x
Hence, ABD is an isosceles triangle with sides AD = BD
and we know that BD = BC
so AD = BD = BC
Statement 1 SUFFICIENT
As AD = 6 = BC
Statement 2 INSUFFICIENT
No information about the length of BC is provided.
Hence the answer is A
