Question

lm = x + 12 ln = x + 15
find mn

Explanation:

Step1: Recall segment addition postulate

For collinear points \( L \), \( M \), \( N \) (where \( M \) is between \( L \) and \( N \)), we have \( LN = LM + MN \).

Step2: Substitute given expressions

We know \( LM = x + 12 \), \( LN = x + 15 \). Substitute into the equation: \( x + 15=(x + 12)+MN \).

Step3: Solve for \( MN \)

Subtract \( x + 12 \) from both sides: \( MN=(x + 15)-(x + 12) \). Simplify: \( MN=x + 15 - x - 12 = 3 \).

Answer:

\( 3 \)