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