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प्रश्न
Find all the angles of the given cyclic quadrilateral ABCD in the figure.
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उत्तर
In a cyclic quadrilateral ABCD,
∠B + ∠D = 180° ...(Sum of the opposite angles of a cyclic quadrilateral is 180°)
6x – 4° + 7x + 2° = 180°
13x – 2° = 180°
13x = 182°
x = 182°
x = `(182^circ)/13`
x = 14°
∠B = 6x – 4°
= 6(14) – 4°
= 84 – 4
= 80°
∠D = 7x + 2°
= 7(14) + 2°
= 98 + 2
= 100°
2y + 4° + 4y – 4° = 180° ...(Sum of the opposite angles of a cyclic quadrilateral is 180°)
6y = 180°
y = `(180^circ)/6`
= 30°
∠A = 2y + 4°
= 2(30) + 4°
= 64°
∠C = 4y – 4°
= 4(30) – 4°
= 120° – 4°
= 116°
∴ ∠A = 64°, ∠B = 80°, ∠C = 116°, ∠D = 100°.
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संबंधित प्रश्न
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ABCD is a parallelogram. The circle through A, B and C intersect CD (produced if necessary) at E. Prove that AE = AD.
Prove that the perpendicular bisectors of the sides of a cyclic quadrilateral are concurrent.
ABCD is a cyclic quadrilateral in which BA and CD when produced meet in E and EA = ED. Prove that EB = EC.
ABCD is a cyclic quadrilateral such that AB is a diameter of the circle circumscribing it and ∠ADC = 140º, then ∠BAC is equal to ______.
ABCD is a cyclic quadrilateral such that ∠A = 90°, ∠B = 70°, ∠C = 95° and ∠D = 105°.
ABCD is a parallelogram. A circle through A, B is so drawn that it intersects AD at P and BC at Q. Prove that P, Q, C and D are concyclic.
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