Data Sufficiency : Geometry

The answer would be C , both statements together are sufficient

soln -

On point B , draw a line EF parallel to AC

from point 2 , X = 36 , so in triangle BDC angle DBC = 36

then angle FBC = 72 ( since angle BCD = 72 )

triangle BDC is isosceles , so BD=BC

similarly angle EBA = 36 ( since angle BAD = 36 )

from this it can be concluded that angle ABD = 36

that means triangle ABD is isosceles too

thus , AD = BD

now from point 1 AD = 6

so , BD = BC = 6

stmnt 1: AD=6
for triangle ABD, angle BDC 2x is an exterior angle. angle ABD=x (sum of 2 interior opposite angles=exterior angle, 2x=x+x)
AD=BD=6 (sides opposite equal angles are equal and vice versa)
BD=BC=6 (sides opposite equal angles are equal and vice versa)
sufficient


stmnt 2: angle x=36
we know AD=BD=BC, but since no information on any length is given, cant find length of BC. not sufficient

hence A