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?
options: 32°, 38°, 48°, 76°

Explanation:

Step1: Use angle bisector property

Since \(UW\) is the angle bisector of \(\angle VUT\), we have \(m\angle VUW = m\angle WUT\). So, \(4x + 6 = 6x - 10\).

Step2: Solve for \(x\)

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

Step3: Find \(m\angle WUT\)

Substitute \(x = 8\) into \(m\angle WUT = (6x - 10)^\circ\): \(6(8) - 10 = 48 - 10 = 38^\circ\).

Answer:

\(38^\circ\)