In a circle with centre O, ABCD is a cyclic quadrilateral and AC is the diameter. Chords AB and DC are produced to meet at E. If ∠CAE = 34° and ∠E = 30°, then ∠CBD is equal to:

Answer: Option C

In, ΔBCE
∠B + ∠C + ∠E = 180°
90° + ∠C + 30° = 180°
∠C = 60°
In, ΔABC
∠A + ∠B + ∠C = 180°
34° + 90° + ∠C = 180°
∠C = 56°
∠ACD = 64° = ∠ABD
∠CBD = 90° - 64° = 26°