Question

In parallelogram MNOP, the diagonals MO and NIP 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 \( ML = LO \).

Given that:
- \( ML = x + 7 \)
- \( LO = 2x - 10 \)

Since \( ML = LO \), we can set up the equation:

\[
x + 7 = 2x - 10
\]

Now, let's solve for \( x \). First, we can subtract \( x \) from both sides:

\[
7 = x - 10
\]

Next, we add 10 to both sides:

\[
7 + 10 = x
\]

\[
17 = x
\]

Thus, the value of \( x \) is:

\[
\boxed{17}
\]