Answer: [tex](\frac{1080}{11})^{\circ}[/tex] and [tex](\frac{900}{11} )^{\circ}[/tex]
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.
[tex]6x + 5x + 90^{\circ} = 180^{\circ}[/tex]
[tex]\implies 11 x + 90^{\circ} = 180^{\circ}[/tex]
[tex]\implies 11x = 90^{\circ}[/tex]
[tex]\implies x = \frac{90}{11}[/tex]
⇒ The one angle of rhombus = [tex](6\times \frac{90}{11})^{\circ}=(\frac{540}{11})^{\circ}[/tex]
And another angle = [tex](5\times \frac{90}{11})^{\circ}=(\frac{450}{11})^{\circ}[/tex]
