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 )? ( \bigcirc 32^circ ) ( \bigcirc 38^circ ) ( \bigcirc 48^circ ) ( \bigcirc 76^circ )

Explanation:

Step1: Set angles equal (bisector)

Since UW bisects \( \angle VUT \), \( m\angle VUW = m\angle WUT \). So, \( 4x + 6 = 6x - 10 \).

Step2: Solve for x

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

Step3: Find \( m\angle WUT \)

Substitute \( x = 8 \) into \( 6x - 10 \): \( 6(8) - 10 = 48 - 10 = 38 \).

Answer:

\( 38^\circ \) (Option: 38°)