Question
) Use the image to answer the question. M P N L (1 point) < Item 19 In parallelogram MNOP, the diagonals MO and NP intersect at point L. ML+7 and LO2z10. What is the value of x? 4
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Answered by
GPT-4o mini
To find the value of \( x \) in the parallelogram \( MNOP \) where the diagonals \( MO \) and \( NP \) intersect at point \( L \), we can use the properties of parallelograms.
In a parallelogram, the diagonals bisect each other, meaning that:
\[
ML = LO
\]
From the information given:
- \( ML = x + 7 \)
- \( LO = 2x - 10 \)
Since \( ML = LO \), we can set the two expressions equal to each other:
\[
x + 7 = 2x - 10
\]
Now, let's solve for \( x \):
1. Subtract \( x \) from both sides:
\[
7 = x - 10
\]
2. Add \( 10 \) to both sides:
\[
7 + 10 = x
\]
\[
x = 17
\]
Thus, the value of \( x \) is \( 17 \).
In a parallelogram, the diagonals bisect each other, meaning that:
\[
ML = LO
\]
From the information given:
- \( ML = x + 7 \)
- \( LO = 2x - 10 \)
Since \( ML = LO \), we can set the two expressions equal to each other:
\[
x + 7 = 2x - 10
\]
Now, let's solve for \( x \):
1. Subtract \( x \) from both sides:
\[
7 = x - 10
\]
2. Add \( 10 \) to both sides:
\[
7 + 10 = x
\]
\[
x = 17
\]
Thus, the value of \( x \) is \( 17 \).
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