$A B C D$ is a cyclic quadrilateral. Find the angle A of the cyclic quadrilateral

80

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100

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110

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120

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Solution

The correct option is C $120$
In cyclic quadrilateral sum of opposite angles is $180$
$- 4 x + 4 y + 20 = 180 ⟹ y - x = 40 y = 40 + x - 7 x + 5 + 3 y - 5 = 0 7 x - 3 y + 180 = 0 7 x - 3 (40 + x) + 180 = 0 4 x + 60 = 0 x = - 15 ⟹ y = 25 ∠ A = 4 (25) + 20 = 120$

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