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  1. If ABCD be a cyclic quadrilateral in which ∠A = 4x°, ∠B = 7x°, ∠C = 5y°, ∠D = y°, then x : y is
    1. 3 : 4
    2. 4 : 3
    3. 5 : 4
    4. 4 : 5
Correct Option: B

According to question , we draw a figure of cyclic quadrilateral ABCD ,

Given that , ∠A = 4x°, ∠B = 7x°, ∠C = 5y°, ∠D = y°,
We know that the sum of opposite angles of a concyclic quadrilateral is 180°.
∴ ∠A + C = 180°
⇒ 4x + 5y = 180° ...(i)
∠B + ∠D = 180°
⇒ 7x + y = 180° ...(ii)
By equation (ii) × 5 – (i),

x =
720
31

From equation (ii),
7x + y = 180°
⇒ 7 ×
720
+ y = 180°
31

y = 180° -
5040
31

y =
5580 - 5040
=
540
3131

∴ x : y =
720
:
540
= 4 : 3
3131



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