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? 32° 38° 48° 76°

Explanation:

Step1: Use angle - bisector property

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

Step2: Solve for x

Subtract \(4x\) from both sides: \(6 = 6x-4x - 10\), which simplifies to \(6 = 2x-10\). Then add 10 to both sides: \(6 + 10=2x\), so \(16 = 2x\). Divide both sides by 2, we get \(x = 8\).

Step3: Find \(m\angle WUT\)

Substitute \(x = 8\) into the expression for \(m\angle WUT\): \(m\angle WUT=(6x - 10)^{\circ}=(6\times8 - 10)^{\circ}=(48 - 10)^{\circ}=38^{\circ}\times2 = 76^{\circ}\).

Answer:

D. 76°