Question
Construct a quadrilateral PQRS in which PQ = 5cm, QR = 6.5cm, $\angle\text{P}=\angle\text{R}=100^\circ$ and $\angle\text{S}=75^\circ.$
✓
Answer
Steps of construction:Step 1: Draw PQ = 5cm.
Step 2:
$\angle\text{P}+\angle\text{Q}+\angle\text{R}+\angle\text{S}=360^\circ$
$100^\circ+\angle\text{Q}+100^\circ+75^\circ=360^\circ$
$275^\circ+\angle\text{Q}=360^\circ$
$\angle\text{Q}=360^\circ-275^\circ$
$\angle\text{Q}=85^\circ$
Step 3: Make $\angle\text{P}=100^\circ$ and $\angle\text{Q}=85^\circ$
Step 4: With Q as the centre, draw an arc of 6.5cm.
Step 5: Make $\angle\text{R}=100^\circ$
Step 6: Join R and S.
Step 7: Measure $\angle\text{S}=75^\circ$
Then, PQRS is the required quadrilateral.
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