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Question

In the give figure, ABCD is a cyclic quadrilateral in which BC = CD and ∠CBD = 35°. Then, ∠BAD = ?
(a) 65°

(b) 70°
(c) 110°
(d) 90°

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Solution

(b) 70°
BC = CD (given)
BDC = ∠CBD = 35°
In
Δ BCD, we have:
∠BCD + BDC + ∠CBD = 180° (Angle sum property of a triangle)
∠BCD + 35° + 35° = 180°
∠BCD = (180° - 70°) = 110°
In cyclic quadrilateral ABCD, we have:
∠BAD + ∠BCD = 180°

∠BAD + 110° = 180°
∠BAD = (180° - 110°) = 70°

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