Question

find the measure of uv. enter your answer as a number.

Explanation:

Step1: Recognize Angle Bisector Property

Since \( TV \) bisects \( \angle UTW \), and \( UV \perp TU \), \( VW \perp TW \), by the Angle Bisector Theorem (or property of angle bisectors), the distances from a point on the angle bisector to the sides of the angle are equal. So \( UV = VW \).

Step2: Set Up Equation

Set \( 3x - 2 = 4x - 9 \).

Step3: Solve for \( x \)

Subtract \( 3x \) from both sides: \( -2 = x - 9 \).
Add 9 to both sides: \( x = 7 \).

Step4: Find \( UV \)

Substitute \( x = 7 \) into \( 3x - 2 \): \( 3(7) - 2 = 21 - 2 = 19 \).

Answer:

19