Question:
Construct a quadrilateral PQRS, where PQ = 3.5 cm, QR = 6.5 cm, ∠P = ∠R = 105° and ∠S = 75°.
Solution:
We know that the sum of all the angles in a quadrilateral is 360 .
i. e., $\angle \mathrm{P}+\angle \mathrm{Q}+\angle \mathrm{R}+\angle \mathrm{S}=360^{\circ}$
$\Rightarrow \angle \mathrm{Q}=75^{\circ}$
Steps of construction:
Step I : Draw PQ $=3.5 \mathrm{~cm}$.
Step II : Construct $\angle \mathrm{XPQ}=105^{\circ}$ at P and $\angle \mathrm{PQY}=75^{\circ}$ at Q.
Step III : With Q as the centre and radius $6.5 \mathrm{~cm}$, cut off QR $=6.5$
Step IV : At R, draw $\angle \mathrm{QRZ}=105^{\circ}$ such that it meets PX at S.
The quadrilateral so obtained is the required quadrilateral.