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svp [43]
3 years ago
8

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

Mathematics
1 answer:
almond37 [142]3 years ago
6 0

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}

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