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Question
In cyclic quadrilateral ABCD, ∠A = 3∠C and ∠D = 5∠B. Find the measure of each angle of the quadrilateral.
Solution
ABCD is a cyclic quadrilateral.
∴ ∠A + ∠C = 180°
`=>` 3∠C + ∠C = 180°
`=>` 4∠C = 180°
`=>` ∠C = 45°
∵ ∠A = 3∠C
`=>` ∠A = 3 × 45°
`=>` ∠A = 135°
Similarly,
∴ ∠B + ∠D = 180°
`=>` ∠B + 5∠B = 180°
`=>` 6∠B = 180°
`=>` ∠B = 30°
∵ ∠D = 5∠B
`=>` ∠D = 5 × 30°
`=>` ∠D = 150°
Hence, ∠A = 135°, ∠B = 30°, ∠C = 45°, ∠D = 150°
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