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Question
In a cyclic quadrilateral ABCD, it is being given that ∠A = (x + y + 10)°, ∠B = (y + 20)°, ∠C = (x + y – 30)° and ∠D = (x + y)°. Then, ∠B = ?
Options
70°
80°
100°
110°
MCQ
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Solution
80°
Explanation:
In a cyclic quadrilateral, opposite angles are supplementary and sum to 180°.
So, A + C = 180°: (x + y + 10) + (x + y – 30) = 180°
⇒ 2(x + y) – 20 = 180°
⇒ x + y = 100°
Thus, D = x + y = 100° and B + D = 180°
⇒ B = 180° – 100°
= 80°
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