Question

for what value of x is the figure a rhombus?

the value of x is
(simplify your answer. type an integer or a fraction.)

Explanation:

Step1: Recall Rhombus Diagonal Property

In a rhombus, the diagonals bisect the angles, and adjacent angles formed by the diagonals are equal. So, \(8x + 4=13x - 9\).

Step2: Solve for x

Subtract \(8x\) from both sides: \(4 = 5x - 9\).
Add 9 to both sides: \(13 = 5x\).
Divide by 5: \(x=\frac{13}{5}\).

Answer:

\(\frac{13}{5}\)