Question

If ABCD is a cyclic quadrilateral in which AD || BC (In the given figure). Prove that ∠B = ∠C.

 

Answer 1

It is given that, ABCD is cyclic quadrilateral in which AD || BC

 

We have to prove  `angleB = angle C`

Since, ABCD is a cyclic quadrilateral

So,

`angle B + angle D = 180°` and `angle A + angle C = 180°`                                   ..… (1)

`⇒ angleB + angle A ` = 180°  and   `angle C + angle D = 180°`           (Sum of pair of consecutive interior angles is 180°)                  …… (2)

From equation (1) and (2) we have

`angleB + angleD + angleB + angle A ` = 360°  …… (3)

 `angleA + angleC + angleC + angle D ` = 360°   …… (4)

`2angleB + angleD + angleA  = 2 angleC + angleA + angleD`

                        `2angleB = 2angleC`

                          `angleB = angleC`

Hence Proved