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In quadrilateral WXYZ, [tex]WC = 2x + 5[/tex] and [tex]CY = 3x + 2[/tex].

What must [tex]x[/tex] equal for quadrilateral WXYZ to be a parallelogram?

[tex]x =[/tex]

Answer :

In a parallelogram, the diagonals bisect each other. This means that the segments from the point where the diagonals intersect to the opposite vertices are equal in length. Thus, we have:

[tex]$$
WC = CY.
$$[/tex]

Given the expressions:

[tex]$$
WC = 2x + 5 \quad \text{and} \quad CY = 3x + 2,
$$[/tex]

we can set them equal:

[tex]$$
2x + 5 = 3x + 2.
$$[/tex]

Now, solve for [tex]$x$[/tex] step by step:

1. Subtract [tex]$2x$[/tex] from both sides:
[tex]$$
5 = x + 2.
$$[/tex]

2. Next, subtract 2 from both sides to isolate [tex]$x$[/tex]:
[tex]$$
5 - 2 = x \quad \Longrightarrow \quad x = 3.
$$[/tex]

So, the value of [tex]$x$[/tex] must be [tex]$3$[/tex] for quadrilateral [tex]$WXYZ$[/tex] to be a parallelogram.

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