Question

for what value of x is the given parallelogram a rhombus? the given parallelogram is a rhombus when x = \square. (type an integer or a decimal.)

Explanation:

Step1: Set angles equal (rhombus diagonal rule)

A parallelogram is a rhombus if its diagonal bisects the angles, so the two given angles are equal:
$3x - 18 = 2x + 7$

Step2: Solve for x

Subtract $2x$ from both sides:
$3x - 2x - 18 = 7$
Simplify and add 18 to both sides:
$x = 7 + 18$

Answer:

$25$