Question

ch. 1.2 - segment addition postulate
refer to the figures below and the given information to find each measure.
given: ac = 39m
a 2x - 8 b x + 17 c
x =
ab =
bc =

Explanation:

Step1: Apply segment - addition postulate

$AB + BC=AC$. So, $(2x - 8)+(x + 17)=39$.

Step2: Simplify the left - hand side

$2x-8+x + 17=3x + 9$. So, $3x+9 = 39$.

Step3: Solve for x

Subtract 9 from both sides: $3x=39 - 9=30$. Then divide both sides by 3: $x=\frac{30}{3}=10$.

Step4: Find AB

Substitute $x = 10$ into the expression for AB. $AB=2x-8=2\times10 - 8=20 - 8 = 12$m.

Step5: Find BC

Substitute $x = 10$ into the expression for BC. $BC=x + 17=10+17 = 27$m.

Answer:

$x = 10$
$AB = 12$m
$BC = 27$m