The value of x that makes the parallelogram a square is 7.35.
Based on the image:
The parallelogram has one side length marked as "(13x - 5.5)".
The angle at the top vertex is labeled as "(13x - 5.5)°".
For a parallelogram to be a square:
All four sides must be equal in length.
All four angles must be right angles (90 degrees).
From the information given:
We know one side length is "(13x - 5.5)".
We know the angle at the top vertex is "(13x - 5.5)°".
To solve for x:
Set the side length equal to itself: Since all sides in a square are equal, "(13x - 5.5)" must be equal to the length of another side. We can choose any other side, but let's use the opposite side for simplicity.
Set the angles equal to 90°: Since all angles in a square are right angles, "(13x - 5.5)°" must be equal to 90°.
Therefore, we have two equations:
Equation 1: (13x - 5.5) = (13x - 5.5) (This ensures the sides are equal)
Equation 2: (13x - 5.5)° = 90° (This ensures the angles are right angles)
Solving Equation 1: Since both sides of the equation are already identical, this equation simply confirms that the side lengths are equal. It doesn't give us any new information about x.
Solving Equation 2:
Subtract 5.5° from both sides to isolate x: 13x = 95.5°
Divide both sides by 13 to solve for x: x = 7.35
Therefore, the value of x that makes the parallelogram a square is 7.35.