Question

1. find the value of x. using that information, find the measurement of \overline{uv}.

Explanation:

Step1: Use segment addition postulate

$$13 + 6+(2x - 18)=4x-29$$

Step2: Simplify left - hand side

$$(13 + 6-18)+2x=4x-29$$
$$1+2x=4x - 29$$

Step3: Isolate \(x\) terms

Subtract \(2x\) from both sides:
$$1=4x-2x - 29$$
$$1 = 2x-29$$
Add \(29\) to both sides:
$$1 + 29=2x$$
$$30=2x$$
Divide both sides by \(2\):
$$x = 15$$

Step4: Find \(UV\)

Substitute \(x = 15\) into \(2x-18\)
$$UV=2\times15-18$$
$$UV = 30 - 18$$
$$UV=12$$

Answer:

\(x = 15\) and \(UV = 12\)