Question

ABCD is a cyclic quadrilateral such that ∠A+∠B=2(∠C+∠D. If ∠C >30°. Then which of them is correct:-
(A) ∠D≥90°
(B) ∠D 90°

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Answer 1

Answer:

In a cyclic quadrilateral ABCD, ⇒ ∠A + ∠C = 180° ⇒ ∠A = 180° – ∠C ...(i) ⇒ ∠B + ∠D = 180° ⇒ ∠B = 180° – ∠D ...(ii) Also, given that ∠A + ∠B = 2(∠C + ∠D) ⇒ 180° – ∠C + 180° – ∠D = 2(∠C + ∠D) ⇒ 360° = 3(∠C + ∠D) ⇒ ∠C + ∠D = 120° Given ∠C > 30° ⇒ ∠D = 120° – ∠C ⇒ ∠D < 90°

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