Question

unit 1: geometry basics
homework 2: segment additic
this is a 2 - page document!
he diagram below to
er questions 1 and 2.
m n
value of x,

1. if lm = 22 and mn = 15, find lj

37

1. if ln = 54 and lm = 31, find mn.

85

1. if df = 9x - 39, find ef.

d e f
47 3x + 10

Explanation:

Problem 1:

Step1: Apply segment addition postulate (LN = LM + MN)

Given \( LM = 22 \), \( MN = 15 \), so \( LN = LM + MN = 22 + 15 \)

Step2: Calculate the sum

\( 22 + 15 = 37 \)

Step1: Apply segment addition postulate (LN = LM + MN), so \( MN = LN - LM \)

Given \( LN = 54 \), \( LM = 31 \), so \( MN = 54 - 31 \)

Step2: Calculate the difference

\( 54 - 31 = 23 \) (Note: The original handwritten answer 85 is incorrect. The correct calculation is \( 54 - 31 = 23 \))

Step1: Apply segment addition postulate (DF = DE + EF). Given \( DE = 47 \), \( EF = 3x + 10 \), \( DF = 9x - 39 \), so \( 9x - 39 = 47 + 3x + 10 \)

Step2: Simplify the equation

\( 9x - 39 = 3x + 57 \)

Step3: Subtract \( 3x \) from both sides

\( 9x - 3x - 39 = 57 \) → \( 6x - 39 = 57 \)

Step4: Add 39 to both sides

\( 6x = 57 + 39 \) → \( 6x = 96 \)

Step5: Divide both sides by 6

\( x = \frac{96}{6} = 16 \)

Step6: Find EF. Substitute \( x = 16 \) into \( EF = 3x + 10 \)

\( EF = 3(16) + 10 = 48 + 10 = 58 \)

Answer:

\( LN = 37 \)

Problem 2: