Let ∠ABO=∠OBC=x and ∠ACO=∠OCB=y.
As it is given that AB=AC. So,
∠B=∠C
⇒2x=2y
⇒x=y…(i)
In ΔABC,
∠ABC+∠BCA+∠CAB=180o
⇒2x+2y+∠CAB=180o
⇒∠A=180o−2x−2y…(ii)
By using exterior angle property,
∠ACD=∠A+∠B
=180o−2x−2y+2x [From (ii)]
=180o−2y…(iii)
Now, by using angle sum property in △OBC,
∠OBC+∠OCB+∠BOC=180o
⇒x+y+∠BOC=180o
⇒y+y+∠BOC=180o [From (i)]
⇒∠BOC=180o−2y…(iv)