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: Angles are $(\frac{1080}{11}) ^{\circ}$ 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.

Thus, By the property of rhombus,

Diagonals perpendicularly bisect each other.

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

⇒ $11 x + 90^{\circ} = 180^{\circ}$

⇒ $11 x = 90^{\circ}$

⇒ $x = \frac{90}{11}$

Therefore, the  angles formed by diagonals and the sides of the rhombus are $(\frac{540}{11} )^{\circ}$ and $(\frac{450}{11})^{\circ}$

⇒ The angles of rhombus are  $(\frac{1080}{11} )^{\circ}$ and  $(\frac{900}{11})^{\circ}$