Question

Ray UW is the angle bisector of Angle VUT. If the measure of Angle VUW = (4x + 6)° and the measure of Angle WUT = (6x – 10)°, what is the measure of Angle WUT?

Answer 1

Hello! :)

Answer:

$\huge\boxed{38^{\circ}}$

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An angle bisector divides an angle in half, therefore:

m∠VUW ≅ m∠WUT

Set the expressions equal to each other:

4x + 6 = 6x - 10

Subtract 4x from both sides:

6 = 2x - 10

Add 10 to both sides:

16 = 2x

Divide 2 from both sides:

x = 8.

Substitute in the value of "x" into the equation for ∠WUT:

6(8) - 10 = 48 - 10 = 38°.