Answer: The angles are 100 degrees, and 80 degrees.
Here's an explanation:
It says that the ratio of the angles are 4:5. In a rhombus, the opposite angles are equal to each other. So, the it would be (4*2)+(5*2) = 360 degrees, since the ratio symbolizes the angle measurements. So, if you calculate that, then 18 units is 360 degrees. 4 units is 80 degrees, and 5 units is 100 degrees.
A rhombus is a quadrilateral. The angles of the rhombus are 80°, 100°, 80°, and 100°.
A rhombus is a quadrilateral such that the pair of opposite sides of the quadrilateral are parallel, and all the sides of the quadrilateral are equal.
As we know that if the ratio of the angles formed by the diagonals and the sides is 4:5, then the ratio of the angles of the rhombus is also 4:5. Also, the pair of opposite angles of a rhombus are equal to each other. Therefore, the angles of the rhombus are 4x, 5x, 4x, and 5x.
Now, as the sum of adjacent angles of a rhombus is 180. Therefore, we can write the sum as,
[tex]4x+5x=180\\\\ 9x=180\\\\x=20[/tex]
Further, the measure of the angles can be written as,
[tex]4x = 4(20) =80^o\\\\5x = 5(20) =100^o\\\\4x = 4(20) =80^o\\\\5x = 5(20) =100^o\\[/tex]
Hence, the angles of the rhombus are 80°, 100°, 80°, and 100°.
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