Question

Ray UW is the angle bisector of VUT.

Answer 1

Answer:

38°

Step-by-step explanation:

An angle bisector divides the angles into 2 equal parts. Since ray UW is the angle bisector of ∠VUT, it divides ∠VUT into two equal angles ∠VUW and ∠WUT

We are given the measures of both angles.

mVUW = (4x + 6)°  

mWUT = (6x – 10)°

Since,

mVUW = mWUT, we can write:

4x + 6 = 6x - 10

6 + 10 = 6x - 4x

16 = 2x

x = 8

Using the value of 8 in equation of mWUT, we get:

mWUT = (6x – 10)°

= 6(8) - 10

= 48 - 10

= 38°

Thus, the measure of WUT is 38°

Answer 2

Answer:

38°

Step-by-step explanation:

Given: Ray UW is the angle bisector of VUT, $\angle \text{WUT}=(6x-10)^{\circ}$  and $\angle \text{VUW}=(4x+6)^{\circ}$

To find: Measure of WUT

Solution: Consider the figure in the attached pic.

We know that the angle bisector will divide the angle into two equal halves.

So, we have $\angle \text{WUT}=\angle \text{VUW}$

Here, $\angle \text{WUT}=(6x-10)^{\circ}$ , and $\angle \text{VUW}=(4x+6)^{\circ}$

So, we have

$6x-10=4x+6$

$6x-4x=10+6$

$2x=16$

$x=8$

So, $\angle \text{WUT}=(6x-10)^{\circ}=6\times8-10=38^{\circ}$

Hence, $\angle \text{WUT}=38^{\circ}$