Question:
Construct a quadrilateral BDEF, where DE = 4.5 cm, EF = 3.5 cm, FB = 6.5 cm, ∠F = 50° and ∠E = 100°.
Solution:
Steps of construction:
Step I : Draw $\mathrm{EF}=3.5 \mathrm{~cm}$.
Step II : Construct $\angle \mathrm{DEF}=100^{\circ}$ at $\mathrm{E}$.
Step III : With $\mathrm{E}$ as the centre and radius $4.5 \mathrm{~cm}$, cut off $\mathrm{DE}=4.5 \mathrm{~cm}$.
Step IV : Construct $\angle \mathrm{EFB}=50^{\circ}$ at F.
Step V : With F as the centre and radius $6.5 \mathrm{~cm}$, cut off $\mathrm{FB}=6.5 \mathrm{~cm}$.
Step VI : Join BD.
The quadrilateral so obtained is the required quadrilateral.
.png)