Question

for what value of x is the parallelogram a rectangle?

the parallelogram is a rectangle when x = \boxed{\quad}.
(type a whole number.)

(there is a diagram of a rectangle with diagonals, and two angles labeled (6x - 5)° and (5x + 5)°)

Explanation:

Step1: Recall rectangle diagonal property

In a rectangle, the diagonals are equal and bisect each other, so the angles formed by the diagonals with a side are equal. Thus, \(6x - 5 = 5x + 5\).

Step2: Solve for x

Subtract \(5x\) from both sides: \(6x - 5x - 5 = 5x - 5x + 5\) → \(x - 5 = 5\).
Add 5 to both sides: \(x - 5 + 5 = 5 + 5\) → \(x = 10\).

Answer:

\(10\)