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