Question

Ray UW is the angle bisector of VUT.

If mVUW = (4x + 6)° and mWUT = (6x – 10)°, what is the measure of WUT?

32°
38°
48°
76°

Answer 1

38°

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*8-10=38^(\circ)`

Hence,
`\angle \text{WUT}=38^(\circ)`

Answer 2

38°

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°