Question

In quadrilateral WXYZ, WC = 2x + 5 and CY = 3x + 2. What must x equal for quadrilateral WXYZ to be a parallelogram?

Answer 1

3

Explanation:

The diagonals of a parallelogram are congruent. This means that WC = 2x+5 = CY = 3x+2:

2x+5 = 3x+2

Subtract 2x from each side:

2x+5-2x = 3x+2-2x

5 = x+2

Subtract 3 from each side:

5-2 = x+2-2

3 = x

Answer 2

The diagonals of a parallelogram bisect each other.
Therefore WC = CY.
That is,
2x + 5 = 3x + 2
Subtract 2x from each side.
5 = 3x - 2x + 2
5 = x + 2
Subtract from each side.
5 - 2 = x + 2 - 2
3 = x

Answer: x = 3

Hope this helps!