Question

Draw rhombus KLMN such that its side is $4$ cm and $\angle K={75}^o$.

Answer 1

$\angle K+\angle L={180}^o$ [ In rhombus um of adjacent angles are supplementary ]

$\Rightarrow$ ${75}^o+\angle L={180}^o$

$\therefore$ $\angle L={105}^o$

$\Rightarrow$ $\angle K=\angle M={75}^o$ [ Opposite angles are equal ]

$\Rightarrow$ And $\angle L=\angle N={105}^o$

$\Rightarrow$ Draw line segment $KL=4cm$

$\Rightarrow$ Take $K$ as center and draw angle of ${75}^o$

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

$\Rightarrow$ Take $L$ as center and draw angle of ${105}^o$

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

$\Rightarrow$ Join $MN$

$\therefore$ $KLMN$ is required rhombus.