Question

ray uw is the angle bisector of ∠vut. if m∠vuw=(4x + 6)° and m∠wut=(6x - 10)°, what is the measure of ∠wut? 32° 38° 48° 76°

Explanation:

Step1: Use angle - bisector property

Since UW is the angle - bisector of ∠VUT, then m∠VUW=m∠WUT. So, we set up the equation 4x + 6=6x−10.

Step2: Solve the equation for x

Subtract 4x from both sides: 6 = 6x−4x−10, which simplifies to 6 = 2x−10. Then add 10 to both sides: 6 + 10=2x, so 16 = 2x. Divide both sides by 2, we get x = 8.

Step3: Find the measure of ∠WUT

Substitute x = 8 into the expression for m∠WUT. m∠WUT=(6x−10)°. Replace x with 8: m∠WUT=6×8−10=48 - 10=38°.

Answer:

38°