Question

find the value of x that makes the parallelogram a square. round to the nearest hundredth. (13x + 22)° answer:

Explanation:

Step1: Recall square diagonal angle property

In a square, the diagonals bisect the right angles, so the angle formed by the diagonals and the sides is $45^\circ$. The given angle $(13x + 22)^\circ$ equals this value.

Step2: Set up equation

$$13x + 22 = 45$$

Step3: Isolate the variable term

Subtract 22 from both sides:
$$13x = 45 - 22$$
$$13x = 23$$

Step4: Solve for x

Divide both sides by 13:
$$x = \frac{23}{13}$$

Step5: Round to nearest hundredth

Calculate the decimal value and round:
$$x \approx 1.77$$

Answer:

$1.77$