Question:
Construct a quadrilateral PQRS, in which PQ = 4 cm, QR = 5 cm, ∠P = 50°, ∠Q = 110° and ∠R = 70°.
Solution:
Steps of construction:
Step I: Draw $\mathrm{PQ}=4 \mathrm{~cm}$.
Step II : Construct $\angle \mathrm{XPQ}=50^{\circ}$ at $\mathrm{P}$ and $\angle \mathrm{PQY}=110^{\circ}$ at $\mathrm{Q}$.
Step III : With $Q$ as the centre and radius $5 \mathrm{~cm}$, cut off $Q R=5 \mathrm{~cm}$.
Step IV: At R, draw $\angle \mathrm{QRZ}=70^{\circ}$ such that it meets PX at S.
The quadrilateral so obtained is the required quadrilateral.
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