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Question
Find all the angles of the given cyclic quadrilateral ABCD in the figure.
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Solution
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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