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If ABCD be a cyclic quadrilateral in which ∠A = 4x°, ∠B = 7x°, ∠C = 5y°, ∠D = y°, then x : y is
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- 3 : 4
- 4 : 3
- 5 : 4
- 4 : 5
- 3 : 4
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 = | |
31 |
From equation (ii),
7x + y = 180°
⇒ 7 × | + y = 180° | |
31 |
y = 180° - | |
31 |
y = | = | ||
31 | 31 |
∴ x : y = | : | = 4 : 3 | ||
31 | 31 |