Question

1. tv = 10x - 26 and vx = 5x + 9. what is the value of x? 35° -17° -7° 7°

Explanation:

Step1: Determine the relationship between \(TV\) and \(VX\)

Since \(\angle T=\angle VUW\) (corresponding angles for parallel lines \(UY\) and \(TX\)), \(\angle T=\angle UWT\) (given \(UW = UT\)), so \(\triangle TVX\) is an isosceles triangle with \(TV = VX\).

Step2: Set up the equation

Set \(10x - 26=5x + 9\).

Step3: Solve the equation

Subtract \(5x\) from both sides: \(10x-5x - 26=5x-5x + 9\), which simplifies to \(5x-26 = 9\).
Add \(26\) to both sides: \(5x-26 + 26=9 + 26\), so \(5x=35\).
Divide both sides by \(5\): \(x=\frac{35}{5}=7\).

Answer:

\(7\)