Your Answer is

Correct Answer is B

Explanation

Connect AC to get two congruent (SSS) isosceles triangles △ACB and △ACD, so ∠B=∠D=1/2∠A; ∠A is the circumferential angle of ∠BCD, so ∠A= 1/2∠BCD=30°, so the required value is 30/2=15°