ABCD is a convex quadrilateral satisfying AB=BC=CD,AD=DB and ∠BAD=75∘. What is the measure of ∠BCD?

Answer 1

Since AD=DB, triangle ABD is isosceles, so
∠DAB = ∠DBA = 75° and ∠ADB = 30°

Now draw AC, and again we have isosceles triangles ABC and BCD.

∠BCD = 75°

Answer 2

150