Question

Construct a rhombus whose side is 5 cm and one angle is of ${60}^{\circ }$.

Answer 1

$\angle B={60}^{\circ }$ [suppose]
$\angle A+\angle B={180}^{\circ }$ [sum of cointerior angles]
$\angle A+{60}^{\circ }={180}^{\circ }$
$\angle A={120}^{\circ }$
AB = BC = CD = DA = 5 cm
Steps of Construction
Step I: Draw AB = 5 cm.
Step II: Draw ray AY such that $\angle BAY={120}^{\circ }$.
Step III: Mark a point D such that AD = 5 cm.
Step IV: Draw a ray BX such that $\angle ABX={60}^{\circ }$
Step V: Mark a point C such that BC = 5 cm.
Step VI: Join C and D.
$\therefore$ ABCD is required rhombus.