Question

Question 187
Construct a parallelogram ABCD in which AB = 4 cm, BC = 5 cm and $\angle B={60}^{\circ }$.

Answer 1

We know that the opposite sides of a parallelogram are equal.
So, AB = DC = 4 cm
BC = AD = 5 cm
$\angle B={60}^{\circ }$
$\angle A+\angle B={180}^{\circ }$ [sum of cointerior angles]
$\angle A={120}^{\circ }$

Steps of Construction
Step I Draw AB = 4 cm.
Step II Draw ray BX such that $\angle ABX={60}^{\circ }$.
Step III Mark a point C such that BC = 5 cm.
Step IV Draw a ray AY such that $\angle YAB={120}^{\circ }$.
Step V Mark a point D such that AD = 5 cm.
Step VI Join C and D.
Hence, ABCD is required parallelogram.