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Answer :
Since the diagonals of a parallelogram bisect each other, the two segments of each diagonal must be equal in length. In quadrilateral [tex]\(WXYZ\)[/tex], we are given:
- [tex]\(WC = 2x + 5\)[/tex]
- [tex]\(CY = 3x + 2\)[/tex]
Because the diagonals bisect each other, we have
[tex]$$
2x + 5 = 3x + 2.
$$[/tex]
Now, we solve this equation step by step:
1. Subtract [tex]\(2x\)[/tex] from both sides to isolate the term with [tex]\(x\)[/tex]:
[tex]$$
5 = x + 2.
$$[/tex]
2. Next, subtract 2 from both sides to solve for [tex]\(x\)[/tex]:
[tex]$$
5 - 2 = x,
$$[/tex]
[tex]$$
3 = x.
$$[/tex]
Thus, the value of [tex]\(x\)[/tex] is
[tex]$$
x = 3.
$$[/tex]
To verify, substitute [tex]\(x = 3\)[/tex] back into the expressions for [tex]\(WC\)[/tex] and [tex]\(CY\)[/tex]:
- For [tex]\(WC\)[/tex]:
[tex]$$
WC = 2(3) + 5 = 6 + 5 = 11,
$$[/tex]
- For [tex]\(CY\)[/tex]:
[tex]$$
CY = 3(3) + 2 = 9 + 2 = 11.
$$[/tex]
Since both segments are equal ([tex]\(11 = 11\)[/tex]), this confirms that the diagonals bisect each other, and quadrilateral [tex]\(WXYZ\)[/tex] is indeed a parallelogram when [tex]\(x = 3\)[/tex].
- [tex]\(WC = 2x + 5\)[/tex]
- [tex]\(CY = 3x + 2\)[/tex]
Because the diagonals bisect each other, we have
[tex]$$
2x + 5 = 3x + 2.
$$[/tex]
Now, we solve this equation step by step:
1. Subtract [tex]\(2x\)[/tex] from both sides to isolate the term with [tex]\(x\)[/tex]:
[tex]$$
5 = x + 2.
$$[/tex]
2. Next, subtract 2 from both sides to solve for [tex]\(x\)[/tex]:
[tex]$$
5 - 2 = x,
$$[/tex]
[tex]$$
3 = x.
$$[/tex]
Thus, the value of [tex]\(x\)[/tex] is
[tex]$$
x = 3.
$$[/tex]
To verify, substitute [tex]\(x = 3\)[/tex] back into the expressions for [tex]\(WC\)[/tex] and [tex]\(CY\)[/tex]:
- For [tex]\(WC\)[/tex]:
[tex]$$
WC = 2(3) + 5 = 6 + 5 = 11,
$$[/tex]
- For [tex]\(CY\)[/tex]:
[tex]$$
CY = 3(3) + 2 = 9 + 2 = 11.
$$[/tex]
Since both segments are equal ([tex]\(11 = 11\)[/tex]), this confirms that the diagonals bisect each other, and quadrilateral [tex]\(WXYZ\)[/tex] is indeed a parallelogram when [tex]\(x = 3\)[/tex].
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