Question

ray uw is the angle bisector of ∠vut.
if m∠vuw = (4x + 6)° and m∠wut = (6x - 10)°, what is the measure of ∠wut?
76°
48°
38°
32°

Explanation:

Step1: Use the angle - bisector property

Since ray \(UW\) is the angle bisector of \(\angle VUT\), then \(m\angle VUW=m\angle WUT\).
Given \(m\angle VUW=(4x + 6)^{\circ}\) and \(m\angle WUT=(6x-10)^{\circ}\), we set up the equation \(4x + 6=6x-10\).

Step2: Solve the equation for \(x\)

Subtract \(4x\) from both sides: \(6=2x - 10\).
Add \(10\) to both sides: \(16 = 2x\).
Divide both sides by \(2\): \(x = 8\).

Step3: Find \(m\angle WUT\)

Substitute \(x = 8\) into the expression for \(m\angle WUT\).
\(m\angle WUT=(6x-10)^{\circ}\), so \(m\angle WUT=(6\times8 - 10)^{\circ}=(48-10)^{\circ}=38^{\circ}\).

Answer:

\(38^{\circ}\)