Question

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

Explanation:

Step1: Use the angle - bisector property

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

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 the measure of \(\angle WUT\)

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

Answer:

B. \(38^{\circ}\)