Question

Construct a quadrilateral ABCD in which: $\angle \text{A}={120}^{\circ },\angle \text{B}={60}^{\circ },\angle \text{AB}=4cm,BC=4.5cm\text{and}CD=5cm.$

Answer 1

Rough figure is as follow :

Actual figure is constructed as follow

Steps :

1. Draw AB = 4 cm.

2. At A, draw $\angle \text{PAB}={120}^{\circ }$

3. At B, draw $\angle \text{QBA}={60}^{\circ }$

4. From BQ, cut BC = 4.5 cm.

5. From C, draw an arc of radius 5 cm which meets AP at D.

6. Join CD.

Thus ABCD is the required quadrilateral.