Question

question 6 (5 points)
listen
find the value of x and ab if \\( \overleftrightarrow { st } \\) is a segment bisector of \\( \overline { ab } \\).
a) \\( x = 4, a b = 120 \\)
b) \\( x = 4, a b = 180 \\)
c) \\( x = 9, a b = 60 \\)
d) \\( x = 9, a b = 180 \\)
question 7 (5 points)

Explanation:

Step1: Set up the equation

Since \(\overrightarrow{ST}\) is a segment bisector of \(\overline{AB}\), then \(AC = CB\). So, \(17x - 8=9x + 24\).

Step2: Solve for \(x\)

Subtract \(9x\) from both sides: \(17x-9x - 8=9x-9x + 24\), which simplifies to \(8x-8 = 24\).
Add \(8\) to both sides: \(8x-8 + 8=24 + 8\), so \(8x=32\).
Divide both sides by \(8\): \(x=\frac{32}{8}=4\).

Step3: Find \(AC\) and \(CB\)

Substitute \(x = 4\) into \(AC=17x - 8\): \(AC=17\times4-8=68 - 8 = 60\).
Substitute \(x = 4\) into \(CB=9x + 24\): \(CB=9\times4+24=36 + 24 = 60\).

Step4: Calculate \(AB\)

Since \(AB=AC + CB\), then \(AB=60+60 = 120\).

Answer:

A. \(x = 4, AB = 120\)