In AOB AO = OB (radius) ∠OAB = ∠OBA (angles opposite to equal sides are equal) ∠OBA = 20° ∠OBC = ∠OCB = 30° (angles opposite to equal sides are equal) ∠ABC = 20 + 30 = 50° ∠AOC = 2 × 50° = 100° (angles subtended by a chord at the center is double the angle subtended at the circumference)