Question

what is the value of x? x =

Explanation:

Step1: Use the Angle - Bisector Theorem (distance from a point to the sides of an angle)

Since \(TV\) is the angle bisector of \(\angle UVW\), and \(TU\perp UV\), \(TW\perp VW\), then \(TU = TW\) (a point on the angle bisector is equidistant from the sides of the angle).

Step2: Set up the equation

We have the equation \(9x - 71=7x - 39\).

Step3: Solve the equation for \(x\)

Subtract \(7x\) from both sides: \(9x-7x - 71=7x - 7x- 39\), which simplifies to \(2x-71=- 39\).
Add \(71\) to both sides: \(2x-71 + 71=-39 + 71\), so \(2x = 32\).
Divide both sides by \(2\): \(x=\frac{32}{2}=16\).

Answer:

\(x = 16\)