Xbond wrote:Hi there,

I woud like your input about this difficult geometry question. Someone can explain to me in simple way the concept. Sorry, I don't know the answer. Look at the attachment

In triangle ABC above, what is the length of side BC ?
(1) The measure of angle AD has length 6.
(2) x = 36

what do u mean by
(1) The measure of angle AD has length 6.

I came up with A as the answer.

from the diagram,
Angle ABC = 180-x-2x = 180-3x
Angle DBC = 180-2x-2x = 180-4x
so, Angle ABD = ABC - DBC = (180-3x) - (180-4x) = x
since ABD = BAD = x, side BD = AD
since BDC = BCD = 2x, side BD = BC
combining these two, side BC = BD = AD

Statement (1) gives AD = 6, so BC = AD = 6
eliminate choice B, C, and E

Statement (2) gives only the degree of the angles, which can prove that Angle B = C = 72 degree, but that doesn't provide the length of BC
eliminate choice D

Answer is A. Is this correct?

sorry, in statement 1, you have to read "the measure of segment AD has lenght 6. the right answer is A