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Answer :
To find the value of [tex]$x$[/tex], we use the fact that in a parallelogram, opposite sides are equal in length.
Given the expressions for the sides:
[tex]$$
WC = 2x + 5 \quad \text{and} \quad CY = 3x + 2
$$[/tex]
Since [tex]$WC$[/tex] and [tex]$CY$[/tex] are opposite sides, we set them equal to each other:
[tex]$$
2x + 5 = 3x + 2
$$[/tex]
Now, solve the equation step-by-step:
1. Subtract [tex]$2x$[/tex] from both sides to isolate the variable term on one side:
[tex]$$
2x + 5 - 2x = 3x + 2 - 2x \quad \Longrightarrow \quad 5 = x + 2
$$[/tex]
2. Subtract [tex]$2$[/tex] from both sides to solve for [tex]$x$[/tex]:
[tex]$$
5 - 2 = x + 2 - 2 \quad \Longrightarrow \quad 3 = x
$$[/tex]
Thus, the value of [tex]$x$[/tex] is:
[tex]$$
\boxed{3}
$$[/tex]
As a check, substitute [tex]$x = 3$[/tex] back into the expressions:
[tex]$$
WC = 2(3) + 5 = 6 + 5 = 11
$$[/tex]
[tex]$$
CY = 3(3) + 2 = 9 + 2 = 11
$$[/tex]
Both expressions equal [tex]$11$[/tex], confirming that [tex]$x = 3$[/tex] is the correct value for [tex]$WXYZ$[/tex] to be a parallelogram.
Given the expressions for the sides:
[tex]$$
WC = 2x + 5 \quad \text{and} \quad CY = 3x + 2
$$[/tex]
Since [tex]$WC$[/tex] and [tex]$CY$[/tex] are opposite sides, we set them equal to each other:
[tex]$$
2x + 5 = 3x + 2
$$[/tex]
Now, solve the equation step-by-step:
1. Subtract [tex]$2x$[/tex] from both sides to isolate the variable term on one side:
[tex]$$
2x + 5 - 2x = 3x + 2 - 2x \quad \Longrightarrow \quad 5 = x + 2
$$[/tex]
2. Subtract [tex]$2$[/tex] from both sides to solve for [tex]$x$[/tex]:
[tex]$$
5 - 2 = x + 2 - 2 \quad \Longrightarrow \quad 3 = x
$$[/tex]
Thus, the value of [tex]$x$[/tex] is:
[tex]$$
\boxed{3}
$$[/tex]
As a check, substitute [tex]$x = 3$[/tex] back into the expressions:
[tex]$$
WC = 2(3) + 5 = 6 + 5 = 11
$$[/tex]
[tex]$$
CY = 3(3) + 2 = 9 + 2 = 11
$$[/tex]
Both expressions equal [tex]$11$[/tex], confirming that [tex]$x = 3$[/tex] is the correct value for [tex]$WXYZ$[/tex] to be a parallelogram.
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