In parallelogram MNOP, the diagonals MO and NIP intersect at point L.

Question

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:

\[ \boxed{17} \]