Question

In the quadrilateral ABCD, ∠A +∠C is 3 times ∠B + ∠D .If ∠A =120° and ∠D = 60° and then ∠B?
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Answer 1

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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 .

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