Question:
Construct a quadrilateral ABCD, in which AB = BC = 3 cm, AD = 5 cm, ∠A = 90° and ∠B = 105°.
Solution:
Steps of construction:
Step I : Draw $\mathrm{AB}=3 \mathrm{~cm}$.
Step II : Construct $\angle \mathrm{DAB}=90^{\circ}$ at A.
Step III : With A as the centre and radius $5 \mathrm{~cm}$, cut off $\mathrm{AD}=5 \mathrm{~cm}$.
Step IV : Construct $\angle \mathrm{ABC}=105^{\circ}$ at B.
Step V : With B as the centre and radius $3 \mathrm{~cm}$, cut off BC $=3 \mathrm{~cm}$.
Step VI : Join CD.
The quadrilateral so obtained is the required quadrilateral.
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