Answer:
The measure of angle WUT is 38°.
Step-by-step explanation:
Given:
m∠ VUW = (4x + 6)°
m∠ WUT = (6x - 10)°
Ray UW is the angle bisector of VUT.
To Find:
m∠ WUT = ?
Solution:
Angle Bisector:
A line that splits an angle into two equal angles.
Bisect means to divide into two equal parts.
∴ m∠ VUW = m∠ WUT
On substituting the values we get
[tex](4x+6)=(6x-10)\\\\6x-4x=10+6\\\\2x=16\\\\\therefore x=\frac{16}{2}=8[/tex]
So on substituting 'x' in angle WUT we get,
[tex]m\angle WUT = 6\times 8 - 10\\\\m\angle WUT =48-10\\\\m\angle WUT =38\°[/tex]
The measure of angle WUT is 38°.
