Quadrilateral abcd is a kite find the measure of angle bcd

If ABCD is a kite, then ∠A and ∠C must be equal to each other.
∠A = ∠C, so ∠C = 87°.

ABCD is a quadrilateral, so all of its interior angles must add up to 360°. We know 3 of the 4 angles, so we'll add them up and subtract the answer from 360.

∠A + ∠C + ∠D ⇒ 87 + 87 + 115 = 289
360 - 289 = 71

m∠B = 71°