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

Question

05-11-2026
Mathematics

Answered

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

Verified Answer :

Related Questions

France yearned for against Germany to regain its position as Europes leading power a truce c revenge b ties d reparations Nations making political and military

Jan noticed at the store that a sweater costs 395 more than a shirt She bought 3 shirts and 2 sweaters and the total cost before tax was 7165 Whats the price of

Algebraic expression for v squared

y7y6 Im not sure how to solve this

2 The relationship between a cathode and an anode involves

7 Which of the following statements best characterizes the European presence in Africa in the first half of the twentieth century With the exception of a few te

a town in otago where a lot of gold was found

Thanks for all the help Which property of the water molecule causes two water molecules to be attracted to other

Which of the following uses punctuation correctly My father advised me that Life is not always fair My father advised me that Life is not always fair My father

How did the growth of the rail networks impact the meatpacking industry

GinnyAnswer GinnyAnswer · Answer 1 · 2026-11-05T12:35:23-05:00

Recognize that for a quadrilateral to be a parallelogram, its diagonals must bisect each other, meaning the point of intersection \(C\) is the midpoint of diagonal \(WY\).
Establish the equation \(WC = CY\) based on the given expressions \(2x+5\) and \(3x+2\).
Solve the equation \(2x+5 = 3x+2\) to find \(x = 3\).
Confirm the validity by verifying that both segments result in positive lengths of 11.
Final answer: \(\boxed{3}\).

Explanation

Analyze properties of a parallelogram

To determine the value of \(x\) that makes the quadrilateral \(WXYZ\) a parallelogram, we must rely on the fundamental properties of parallelograms. One essential property is that the diagonals of a parallelogram bisect each other. This means that the point of intersection of the diagonals, which is point \(C\) in this case, must be the midpoint of each diagonal.

Given that point \(C\) lies on the diagonal \(WY\), for \(WXYZ\) to be a parallelogram, \(C\) must be the midpoint of \(WY\). Consequently, the length of segment \(WC\) must be equal to the length of segment \(CY\). We are provided with the expressions for these lengths:
\(WC = 2x + 5\)
\(CY = 3x + 2\)

Set up and solve the equation for x

We set the lengths of the segments equal to each other to solve for \(x\):
\[2x + 5 = 3x + 2\]

Subtract \(2x\) from both sides of the equation:
\[5 = x + 2\]

Subtract 2 from both sides of the equation:
\[x = 3\]

Thus, the value of \(x\) that satisfies the condition for the diagonal segments is \(x = 3\).

Verify the results

To ensure the result is geometrically valid, we must verify that the segment lengths are positive for \(x = 3\):
\(WC = 2(3) + 5 = 6 + 5 = 11\)
\(CY = 3(3) + 2 = 9 + 2 = 11\)

Since both segments have a length of 11, which is greater than zero, the condition for the diagonal bisecting is satisfied. Thus, the value of \(x\) for which \(WXYZ\) is a parallelogram is \(x = 3\). The final answer is \(\boxed{3}\).

Examples

In structural engineering and architecture, understanding the properties of a parallelogram is crucial for ensuring stability in frames. For example, if you are designing a bridge truss or a hinged gate that must maintain a constant shape while shifting, ensuring that the diagonals bisect each other allows for smooth, predictable motion. By setting the diagonal segments correctly, such as \(WC = CY = 11\), you guarantee the geometric integrity of the design.