If ABCD be a cyclic quadrilateral in which ∠A = 4x°,

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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
	31		31

∴ x : y =	720	:	540	= 4 : 3
	31		31