Question

for what value of x is the given parallelogram a rhombus?
the given parallelogram is a rhombus when x =
(5x + 22)°
(8x - 8)°

Explanation:

Step1: Recall rhombus property

In a rhombus, the diagonals bisect the angles. So the two angle expressions \((5x + 22)^\circ\) and \((8x - 8)^\circ\) are equal.
Set up the equation: \(5x + 22 = 8x - 8\)

Step2: Solve for x

Subtract \(5x\) from both sides: \(22 = 3x - 8\)
Add 8 to both sides: \(30 = 3x\)
Divide by 3: \(x = 10\)

Answer:

\(10\)