anyone knows how option 1 is also suff.?
I dont think I would have initially guessed D. But spending about 7min on this in detail, I can see why D is the answer.
AB=OC=BO=OX=AX X is the midpoint of OA
So now we have two iscocoles triangles.
Lets name the angles with variables: OCB=y OBC=y BCO=z
BAO=x BOA=x ABO=w
(its obviously much easier to draw these)
We need to write the appropriate eqautions out. 2y+z=180, 2x+w=180
y+w=180, Since we know COD=60* We know that x+z=120*
We have 4 equations and 4 unknowns. Should be enough. Lets solve anyway. We want to know what x=?
z=120-x 2y+120-x=180 --> 2y-x=60 x=2y-60.
w=180-2x --> y+180-2x=180--> y-2x=0 --> y=2x So x=2(2x)-60
-3x=-60 ---> x=20.
This one is very easy: we still have the same equations from above.
y+z=180, 2x+w=180, y+w=180
Since y=40* w=140* --> 2x=40* x=20*