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Question
In a quadrilateral ABCD, ∠A + ∠C is 2 times ∠B + ∠D. If ∠A = 140° and ∠D = 60°, then ∠B=
Options
60°
80°
120°
80°
None of these
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Solution
ABCD is a quadrilateral, with ∠A +∠C = 2(∠B + ∠D) .
By angle sum property of a quadrilateral we get:
∠A +∠B +∠C +∠D = 360°
(∠A +∠C )+(∠B +∠D) = 360°
But,we have ∠A+∠C = 2(∠B +∠D)
2(∠A + ∠C = 360°
∠A + ∠C = 120°
Then,
∠B + ∠D = 60°
The two equations so formed cannot give us the value for ∠B with a given value of ∠A .
Hence the correct choice is (d).
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