Question

Construct a quadrilateral ABCD, where AB = 5.5 cm, BC = 3.7 cm, ∠A = 60°, ∠B = 105° and ∠D = 90°.

Answer 1

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 .