Question

1. use the image below to find the missing value. using the segment addition postulate, find the value of m. ab = 4m - 15, bc = 5m - 6, ac = 15. options: 15, 36, 4, 9.

Explanation:

Step1: Apply Segment Addition Postulate

The Segment Addition Postulate states that \( AB + BC = AC \). Substitute the given expressions: \( (4m - 15) + (5m - 6) = 15 \).

Step2: Simplify the left side

Combine like terms: \( 4m + 5m - 15 - 6 = 15 \) → \( 9m - 21 = 15 \).

Step3: Solve for \( m \)

Add 21 to both sides: \( 9m = 15 + 21 \) → \( 9m = 36 \). Divide by 9: \( m = \frac{36}{9} = 4 \).

Answer:

4