Question:
Construct a quadrilateral ABCD when BC = 5.5 cm, CD = 4.1 cm, ∠A = 70°, ∠B = 110° and ∠D = 85°.
Solution:
We know that the sum of all the angles in a quadrilateral is 360 .
i. e., $\angle \mathrm{A}+\angle \mathrm{B}+\angle \mathrm{C}+\angle \mathrm{D}=360^{\circ}$
$\Rightarrow \angle \mathrm{C}=95^{\circ}$
Steps of construction:
Step I : Draw BC $=5.5 \mathrm{~cm}$.
Step II : Construct $\angle \mathrm{XBC}=110^{\circ}$ at A and $\angle \mathrm{BCY}=95^{\circ}$.
Step III : With C as the centre and radius $4.1 \mathrm{~cm}$, cut off CD $=4.1 \mathrm{~cm}$.
Step IV : At D, draw $\angle \mathrm{CDZ}=85^{\circ}$ such that it meets BY at A.
The quadrilateral so obtained is the required quadrilateral.