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° 76° 38° 48°

Explanation:

Step1: Set equal angles

Since UW is angle - bisector, $m\angle VUW=m\angle WUT$. So, $4x + 6=6x-10$.

Step2: Solve for x

$6 + 10=6x-4x$, $16 = 2x$, $x = 8$.

Step3: Find $m\angle WUT$

Substitute $x = 8$ into $m\angle WUT=6x - 10$, $m\angle WUT=6\times8-10=48 - 10=38^{\circ}$.

Answer:

$38^{\circ}$