In a quadrilateral ABCD, ∠A + ∠C is 2 times ∠B + ∠D. If ∠A = 140° and ∠D = 60°, then ∠B =

(a) 60°

(b) 80°

(c) 120°

(d) None of these

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Solution

ABCD is a quadrilateral, with.

By angle sum property of a quadrilateral we get:

But,we have

Then,

The two equations so formed cannot give us the value for with a given value of .

Hence the correct choice is (d).

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Similar questions

In a quadrilateral ABCD, $∠ A + ∠ C$ is 2 times $∠ B + ∠ D$ . If $∠ A = 140^{\circ} a n d ∠ D = 60^{\circ}, t h e n ∠ B =$

In quadrilateral ABCD, side AB is parallel to side DC and ∠A : ∠D = 1 : 2 and ∠C : ∠B = 4 : 5. Measure of angles of quadrilateral ABCD are

The following figure shows a quadrilateral with sides AB and DC parallel to each other.

If $∠ A : ∠ D = 4 : 5$

$∠ B = (3 x - 15)^{\circ} a n d$

$∠ C = (4 x + 20)^{\circ}$

Which of the following options is/are correct ?

A B C D

∠

A

60^{\circ}

∠ A = 60^{\circ}

∠ B : ∠ C : ∠ D = 2 : 4 : 6

∠ C .

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