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