Question

If ABCD is a cyclic quadrilateral in which AD || BC. Prove that ∠B = ∠C.

Answer 1

ABCD is a cyclic quadrilateral.
So, ∠A + ∠C = 180°        ...(i)

Since AD || BC
So, ∠B + ∠A = 180°       ....(ii)

From (i) and (ii)
∠A + ∠C = ∠B + ∠A
∠C = ∠B
or ∠B = ∠C
Hence proved.