Question

Construct a rhombus with side $4$ cm and one of its angles equal to ${45}^o$.

Answer 1

$\angle A+\angle B={180}^o$ [ Sum of adjacent angles in rhombus is ${180}^o$ ]

$\Rightarrow$ ${45}^o+\angle B={180}^o$

$\therefore$ $\angle B={135}^o$

$\Rightarrow$ $\angle A=\angle C$ and $\angle B=\angle D$ [ Opposite angles are equal ]

$\Rightarrow$ Draw a line segment $AB=4cm$

$\Rightarrow$ Take $A$ as center and draw angle of ${45}^o$

$\Rightarrow$ Cut off $AD=4cm$

$\Rightarrow$ Take $B$ as center and draw angle of ${135}^o$

$\Rightarrow$ Cut off $BC=4cm$

$\Rightarrow$ Join $CD$

$\therefore$ $ABCD$ is a required rhombus.