Question

m is a point on segment (overline{ln}). if (lm = 20), (mn = x + 1), and (ln = 2x + 9), what is (mn)? simplify your answer and write it as a proper fraction, mixed number, or integer.

Explanation:

Step1: Apply segment addition postulate

Since \( M \) is on \( \overline{LN} \), we have \( LM + MN = LN \). Substituting the given values: \( 20+(x + 1)=2x + 9 \).

Step2: Simplify and solve for \( x \)

Simplify left side: \( 20+x + 1=2x + 9\) → \(x + 21=2x + 9\). Subtract \( x \) from both sides: \(21=x + 9\). Subtract 9: \(x = 12\).

Step3: Find \( MN \)

Substitute \( x = 12 \) into \( MN=x + 1 \): \(MN=12 + 1=13\).

Answer:

\( 13 \)