Construct a quadrilateral PQRS, in which ∠Q = 45°,


Construct a quadrilateral PQRS, in which ∠Q = 45°, ∠R = 90°, QR = 5 cm, PQ = 9 cm and Rs = 7 cm.


Steps of construction:

Step I : Draw QR $=5 \mathrm{~cm} .$

Step II : Construct $\angle \mathrm{PQR}=45^{\circ}$ at Q.

Step III : With Q as the centre and radius $9 \mathrm{~cm}$, cut off QP $=9 \mathrm{~cm} .$

Step IV : Construct $\angle \mathrm{QRS}=90^{\circ}$ at R.

Step V : With R as the centre and radius $7 \mathrm{~cm}$, cut off RS $=7 \mathrm{~cm} .$

Since, the line segment PQ and RS intersect each other, the quadrilateral cannot be constructed.

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