Question

For which value of x is the figure a rhombus?

A. X=6
B. X= 7.5
C. X=12
D. X=18.75

Answer 1

That is a question about properties of rhombus.

There is a property of a rhombus that says that the its diagonals divided the internal angles in two equals angles.

Now that we know about it, it is easier to solve this question, because now we know that
`2x+39` and
`6x - 9` are equal angles. So, we can make a equation and solve it:

`2x+39 = 6x - 9\\39 + 9 = 6x - 2x\\48 = 4x\\4x = 48\\x=(48)/(4) \\x=12`

Therefore, the value of
`x` is 12. So, the correct alternative is letter C).

I hope I've helped. ^^

Enjoy your studies! \o/