Step-by-step explanation:

OA = OB [radii of a circle]

∠OAB = ∠OBA [Angles opposite to equal sides of a triangle]

Similarly,

OB = OC [radii of the same circle]

∠OCB = ∠OBC [Angles opposite to equal sides of a triangle]

In

ΔOBC,

∠OBC + ∠OCB + ∠BOC = 180∘ [Angle sum property]

∠BOC = 180∘ - 110∘ = 70∘

In ΔOAB,

∠OAB + ∠OBA + ∠AOC + ∠BOC = 180∘ [Angle sum property]

∠AOC = 180∘ - 20∘- 20∘ - 70∘

= 70∘

So,

∠AOC = ∠BOC = 70∘