In a parallelogram, the diagonals bisect each other. Therefore, the length of diagonal KM is twice the length of segment NM.
Let’s denote the lengths mathematically. We have:
- Length of \( KM = 5x + 1 \)
- Length of \( NM = 2x + 9 \)
Since N is the midpoint of KM, we have:
\[ NM = \frac{1}{2} KM \]
Substituting the expressions for \( KM \) and \( NM \) into the equation gives:
\[ 2x + 9 = \frac{1}{2}(5x + 1) \]
To eliminate the fraction, multiply both sides by 2:
\[ 2(2x + 9) = 5x + 1 \]
Distributing on the left side:
\[ 4x + 18 = 5x + 1 \]
Now, let’s solve for \( x \). First, subtract \( 4x \) from both sides:
\[ 18 = 5x - 4x + 1 \]
This simplifies to:
\[ 18 = x + 1 \]
Now, subtract 1 from both sides:
\[ 17 = x \]
Thus, the value of \( x \) is:
\[ \boxed{17} \]