Question

In a cyclic quadrilateral ABCD, if AD||BC then prove that angle A = angle D

(please solve that ques. guys!)​

Answer 1

$\LARGE\mathfrak\pink{answer}$

ABCD is a cyclic quadrilateral on which AD || BC

To Be proved :

• ∠A = ∠D

Proof : ABCD is a cyclic quadrilateral

• We know that the sum of opposite angles of a cyclic quadrilateral is 180°

$\:$ ∠A + ∠C = 180°

and ∠B + ∠D = 180° ... (ii)

but ∠A + ∠B = 180° {co - interior corresponding angles} (iii)

From equation (ii) and (iii)

$\:$ 2∠A + ∠B + ∠C = ∠B + ∠C + 2∠D

$\:$ 2∠A = 2∠D

$\:$ ∠A = ∠D

$\large\rm{Hence\:Proved}$✔

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