Question

3) Construct a rhombus HIJK such that its side is 5 cm and mZH = 75°.​

Answer 1

$\huge{\underline{ \mathtt{\red{❥A} \green{n}\mathtt\blue{s} \purple{w} \mathtt \orange{e}\pink{r}}}}\:$

∠K+∠L=180 [ In rhombus um of adjacent angles are supplementary ]

⇒ 75 +∠L=180

∴ ∠L=105

o

⇒ ∠K=∠M=75

o

[ Opposite angles are equal ]

⇒ And ∠L=∠N=105

o

⇒ Draw line segment KL=4cm

⇒ Take K as center and draw angle of 75

o

⇒ Cut off KN=4cm

⇒ Take L as center and draw angle of 105

o

⇒ Cut off LM=4cm

⇒ Join MN

∴ KLMN is required rhombus.

Answer 2

$\huge{\underline{ \mathtt{\red{❥A} \green{n}\mathtt\blue{s} \purple{w} \mathtt \orange{e}\pink{r}}}}\:$

∠K+∠L=180 [ In rhombus um of adjacent angles are supplementary ]

⇒ 75 +∠L=180

∴ ∠L=105

o

⇒ ∠K=∠M=75

o

[ Opposite angles are equal ]

⇒ And ∠L=∠N=105

o

⇒ Draw line segment KL=4cm

⇒ Take K as center and draw angle of 75

o

⇒ Cut off KN=4cm

⇒ Take L as center and draw angle of 105

o

⇒ Cut off LM=4cm

⇒ Join MN

∴ KLMN is required rhombus.