Question
Construct a quadrilateral PQRS, in which $\angle\text{PQR}=45^\circ,$ $\angle\text{QRS}=90^\circ,$ QR = 5cm, PQ = 9cm and Rs = 7cm.
✓
Answer
Steps of construction:Step I: Draw QR = 5cm.
Step II: Construct $\angle\text{PQR}=45^\circ$ at Q.
Step III: With Q as the centre and radius 9cm, cut off QP = 9cm.
Step IV: Construct $\angle\text{QRS}=90^\circ$ at R.
Step V: With R as the centre and radius 7cm, cut off RS = 7cm. Since, the line segment PQ and RS intersect each other, the quadrilateral cannot be constructed.
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