Question

In parallelogram MNOP, the diagonals MO and NP intersect at point L. ML=x+7 and LO=2x-10. What is the value of x?

Answer 1

In a parallelogram, the diagonals bisect each other. This means that the segments created by each diagonal are equal.

Here, we have the segments \( ML \) and \( LO \):
- \( ML = x + 7 \)
- \( LO = 2x - 10 \)

Since \( L \) is the midpoint of both diagonals, we can set the two segments equal to each other:
\[
ML = LO
\]
This gives us the equation:
\[
x + 7 = 2x - 10
\]

Now, we will solve for \( x \):
1. Subtract \( x \) from both sides:
\[
7 = 2x - x - 10
\]
Simplifying this results in:
\[
7 = x - 10
\]

2. Add 10 to both sides:
\[
7 + 10 = x
\]
\[
x = 17
\]

Thus, the value of \( x \) is \( \boxed{17} \).