The measure of an angle wut is 38 degrees.
According to the given question.
The measure of an angle vuw, m ∠vuw = (4x + 6) degrees
And, the measure of an angle wut, m ∠wut = (6x - 10) degrees
Given that ray uw is the angle bisector of vut, this means that
m ∠vuw = m ∠wut
⇒ (4x + 6) = (6x - 10)
⇒ 4x + 6 = 6x - 10
⇒ 4x - 6x = -10 - 6
⇒ -2x = -16
⇒ x = -16/-2
⇒ x = 8 degrees
Therefore, measure of an angle wut is given by
m ∠wut
= (6x - 10 )
= ( 6(8) - 10)
= 48 - 10
= 38 degrees
Hence, the measure of an angle wut is 38 degrees.
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