(i)

OB = OC [Radius]

∴ ∠OBC = ∠OCB = 55°

In triangle OCB,

∠OBC + ∠OCB + ∠BOC = 180°[Sum of angles of triangle]

⇒ 55° + 55° + ∠BOC = 180°

⇒ 110° + ∠BOC = 180°

⇒ ∠BOC = 70°

(ii)

OA = OB [Radius]

∴ ∠OBA = ∠OAB = 20°

In triangle AOB,

∠OBA + ∠OAB + ∠AOB = 180°[Sum of angles of triangle]

⇒ 20° + 20° + ∠AOB = 180°

⇒ 40° + ∠AOB = 180°

⇒ ∠AOB = 140°

∴ ∠AOC = ∠AOB - ∠BOC

⇒ ∠AOC = 140° - 70°

⇒ ∠AOC = 70°