Question

Find the angles of the rhombus if the ratio of the angles formed by diagonals and the sides of the rhombus is 6:5.

Answer 1

Answer: $(\frac{1080}{11})^{\circ}$ and $(\frac{900}{11} )^{\circ}$

Step-by-step explanation:

Here, the ratio of the angles formed by diagonals and the sides of the rhombus is 6:5.

Let the angles formed by diagonals and the sides of the rhombus are 6x and 5x.

Where x is any number.

Therefore, the angles of rhombus are = 12 x and 10x ( Because in rhombus opposite angles are equal and diagonals are the angle bisectors in case of rhombus)

Also, In rhombus diagonals bisect each other perpendicularly.

$6x + 5x + 90^{\circ} = 180^{\circ}$

$\implies 11 x + 90^{\circ} = 180^{\circ}$

$\implies 11x = 90^{\circ}$

$\implies x = \frac{90}{11}$

⇒ The one angle of rhombus = $(6\times \frac{90}{11})^{\circ}=(\frac{540}{11})^{\circ}$    

And another angle = $(5\times \frac{90}{11})^{\circ}=(\frac{450}{11})^{\circ}$