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
`((1080)/(11)) ^(\circ)` and
`((900)/(11))^(\circ)`

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 = (90)/(11)`

Therefore, the angles formed by diagonals and the sides of the rhombus are
`((540)/(11) )^(\circ)` and
`((450)/(11))^(\circ)`

⇒ The angles of rhombus are
`((1080)/(11) )^(\circ)` and
`((900)/(11))^(\circ)`