The question is incomplete the complete question is
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:
Therefore,
[tex]m\angle WUT=38\°[/tex]
Step-by-step explanation:
Given:
Ray UW is the angle bisector of VUT.
mAngle VUW = (4x + 6)° and
m AngleWUT = (6x – 10)°
To Find:
Angle WUT = ?
Solution:
Angle Bisector: A line that splits an angle into two equal angles is called angle bisector.
Bisect means to divide into two equal parts.
Ray UW is the angle bisector of VUT. .....Given
Therefore,
[tex]\angle VUW=\angle WUT[/tex]
Substituting the values we get
[tex]4x+6=6x-10\\6x-4x=10+6\\2x=16\\x=\dfrac{16}{2}\\\therefore x=8[/tex]
Now Substituting 'x' value in angle WUT we get
[tex]m\angle WUT=6\times 8-10=48-10=38\°[/tex]
Therefore,
[tex]m\angle WUT=38\°[/tex]
Option B is correct. The measure of angle WUT given that angle VUW = (4x + 6)° and angle WUT = (6x – 10)° is 38 degrees
An angle is formed from the intersection of two lines
Given that Ray UW is the angle bisector of VUT, this means that:
Given the following parameters
<VUW = (4x + 6)°
<WUT = (6x – 10)°
Equating both expressions to get the value of x
4x + 6 = 6x - 10
Collect the like terms
4x - 6x = -10 - 6
-2x = -16
x = 16/2
x = 8
Get the measure of the angle WUT
m<WUT = 6x - 10
m<WUT = 6(8) - 10
m<WUT = 48 - 10
m<WY=UT = 38degrees
Hence the measure of angle WUT given that angle VUW = (4x + 6)° and angle WUT = (6x – 10)° is 38 degrees
Learn more here: https://brainly.com/question/17247176
