upd: here's a pic...

ΔABC is isosceles.

Find X

__WITHOUT__ using trig or algebra, by constructing segments || to those given and such and deriving angles from there, knowing that vertically opposite angles are congruent, etc...

I already solved this prolbem using sine and cosine laws, but that was not acceptable

... Spend days on this one, even tried solving backwards having X be known (from solving it the other way), but still nothing...

i don't want the solution, but if you could just point me in the right direction, get me started, i'd appreciate it!