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Question
Construct a quadrilateral PQRS, where PQ = 3.5 cm, QR = 6.5 cm, ∠P = ∠R = 105° and ∠S = 75°.
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Solution
We know that the sum of all the angles in a quadrilateral is 360 .
i . e . , ∠P + ∠Q + ∠R + ∠S = 360°
⇒ ∠Q = 75°
Steps of construction:
Step I: Draw PQ = 3 . 5 cm .
Step II: Construct ∠XPQ = 105° at P and ∠PQY = 75° at Q .
Step III: With Q as the centre and radius 6 . 5 cm, cut off QR = 6 . 5
Step IV: At R, draw ∠QRZ = 105° such that it meets PX at S .
The quadrilateral so obtained is the required quadrilateral .
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