What special name can be given to a quadrilateral PQRS if ∠P + ∠S = 180°?

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Solution

Since, in quadrilateral PQRS, ∠P + ∠S = 180°.

i.e. the sum of adjacent angles is 180 $°$ .

So, PQRS is a parallelogram.

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A B C D, ∠ A + ∠ D = 180^{\circ} .

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∠ A + ∠ D = 180^{\circ}

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In quadrilateral PQRS, $∠ P : ∠ Q : ∠ R : ∠ S = 3 : 4 : 6 : 7$ .

Calculate each angle of the quadrilateral and then prove that PQ and SR are parallel to each other.

(i) Is PS also parallel to QR ?

(ii) Assign a special name to quadrilateral PQRS.

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