Given: and

Here,

In ΔAOB

OA = OB (radius)

∠OAB = ∠OBA (angles opposite to equal sides are equal)

∴ ∠ OBA = 30°

Now, by angle sum property

∠AOB + ∠OBA + ∠OAB = 180°

∠AOB + 30° + 30° = 180°

∠AOB = 180° – 30° – 30°

∠AOB = 120°

Now, Consider Δ BOC

OC = OB (radius)

∠OCB = ∠OBC (angles opposite to equal sides are equal)

∴ ∠ OBA = 55°

Now, by angle sum property

∠BOC + ∠OBC + ∠OCB = 180°

∠BOC + 55° + 55° = 180°

∠BOC = 180° – 55° – 55° = 70°

∴ ∠BOC = 70°

Here,

∠AOB = ∠AOC + ∠BOC

120° = ∠AOC + 70°

∠AOC = 120° – 70°

∠AOC = 50°

∴ ∠AOC = 50°

∴