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Question
Construct a quadrilateral ABCD, where AB = 5.5 cm, BC = 3.7 cm, ∠A = 60°, ∠B = 105° and ∠D = 90°.
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Solution
We know that the sum of all the angles in a quadrilateral is 360 .
i . e . , ∠A + ∠B + ∠C + ∠D = 360°
⇒ ∠C = 105°
Steps of construction:
Step I: Draw AB = 5 . 5 cm .
Step II: Construct ∠XAB = 60° at A and ∠ABY = 105° .
Step III: With B as the centre and radius 3 . 7 cm, cut off BC = 3 . 7 cm .
Step IV: At C, draw ∠BCZ = 105° such that it meets AX at D .
The quadrilateral so obtained is the required quadrilateral .
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