Question:
Construct a quadrilateral PQRS, in which PQ = 3.5 cm, QR = 2.5 cm, RS = 4.1 cm, ∠Q = 75° and ∠R = 120°.
Solution:
Steps of construction:
Step I : Draw QR $=2.5 \mathrm{~cm}$.
Step II : Construct $\angle \mathrm{PQR}=75^{\circ}$ at Q.
Step III : With Q as the centre and radius $3.5 \mathrm{~cm}$, cut off QP $=3.5 \mathrm{~cm}$.
Step IV : Construct $\angle \mathrm{QRS}=120^{\circ}$ at R.
Step V : With R as the centre and radius $4.1 \mathrm{~cm}$, cut off RS $=4.1 \mathrm{~cm}$.
Step VI : Join PS
The quadrilateral so obtained is the required quadrilateral.
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