let angle BAO =x so angle BOA = x (ab =oc=ob)

so angle ABO =180 -2x

so angle CBO = angle BCO = 2x

hence angle BOC = 180-4x so angle COA = 180-4x+x =180-3x

and since COD =60degs hence COA =120 =180-3x

x=20

thank you so much..

Hi, samirpandeyit62---

How did you know that AB and BC formed the straight line AC? From the diagram, it looks like a straight line, but my understanding is that we can't always assume the diagram is to scale.

Thx,

K

Hi Kansonne,
As per my knowledge of the directions for geomety questions, we can extract some data from the diagram like here we can say AC is a straight line, coz it clearly looks like that in the diagram, IMO if there was an angle then it would have been clearly shown (you see a lot of geometry questions rely on the fact that sum of two angles along a straight line is 180 degs) i.e AB and BC will appear to make an angle , coz then the ans would be E

Ans... D
1)
angle bao = boa = x
angle obc = ocb = y

Now cod is 60, equal to sum of opposite angles oab and oca
x+y = 60

similarly obc = bao + boa
y = 2x

solve these x = 20.
2) is easy..