Construct a quadrilateral PQRS, in which PQ = 4 cm,

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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