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

The measure of angle WUT is 38°.

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

`(4x+6)=(6x-10)\\\\6x-4x=10+6\\\\2x=16\\\\\therefore x=(16)/(2)=8`

So on substituting 'x' in angle WUT we get,

`m\angle WUT = 6* 8 - 10\\\\m\angle WUT =48-10\\\\m\angle WUT =38\°`

The measure of angle WUT is 38°.