Construct a quadrilateral PQRS, in which PQ = 4 cm, QR = 5 cm, ∠P = 50°, ∠Q = 110° and ∠R = 70°.

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Solution

$Steps of construction : Step I : Draw PQ = 4 cm . Step II : Construct ∠ XPQ = 50 ° at P and ∠ PQY = 110 ° at Q . Step III : With Q as the centre and radius 5 cm, cut off QR = 5 cm . Step IV : At R, draw ∠ QRZ = 70 ° such that it meets PX at S . The quadrilateral so obtained is the required quadrilateral .$

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In a quadrilateral PQRS, PQ = 3 cm, QR = 4 cm and PS = 5 cm. Also, $∠$ SPQ = $70^{\circ}$ and $∠$ PQR = $90^{\circ}$ . Which of the following options is the approximate value of $∠$ QRS?

In the construction of quadrilateral PQRS, with PQ = 3 cm, QR = 4 cm and PS = 5 cm, also, $∠$ SPQ = $70^{\circ}$ and $∠$ PQR = $90^{\circ}$ , which of the sides is to be taken as base and constructed first?

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Construct a quadrilateral PQRS, in which PQ = 4 cm, QR = 5 cm, ∠P = 50°, ∠Q = 110° and ∠R = 70°.

Steps of construction:Step I: Draw PQ=4 cm.Step II: Construct ∠XPQ=50° at P and ∠PQY=110° at Q.Step III : With Q as the centre and radius 5 cm, cut off QR=5 cm.Step IV: At R, draw ∠QRZ=70° such that it meets PX at S. The quadrilateral so obtained is the required quadrilateral.