Question

for what value of x is the given parallelogram a rhombus? the given parallelogram is a rhombus when x = (2x + 48)° (6x - 4)°

Explanation:

Step1: Recall rhombus angle property

In a rhombus, the diagonal bisects the angles, so the two angles \((2x + 48)^\circ\) and \((6x - 4)^\circ\) are equal.
Set up the equation: \(2x + 48 = 6x - 4\)

Step2: Solve for x

Subtract \(2x\) from both sides: \(48 = 4x - 4\)
Add 4 to both sides: \(52 = 4x\)
Divide by 4: \(x = \frac{52}{4} = 13\)

Answer:

13