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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°

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 class=

Respuesta :

SaniShahbaz

Answer:

38°

Step-by-step explanation:

An angle bisector divides the angles into 2 equal parts. Since ray UW is the angle bisector of ∠VUT, it divides ∠VUT into two equal angles ∠VUW and ∠WUT

We are given the measures of both angles.

mVUW = (4x + 6)°  

mWUT = (6x – 10)°

Since,

mVUW = mWUT, we can write:

4x + 6 = 6x - 10

6 + 10 = 6x - 4x

16 = 2x

x = 8

Using the value of 8 in equation of mWUT, we get:

mWUT = (6x – 10)°

= 6(8) - 10

= 48 - 10

= 38°

Thus, the measure of WUT is 38°

aachen

Answer:

38°

Step-by-step explanation:

Given: Ray UW is the angle bisector of VUT, [tex]\angle \text{WUT}=(6x-10)^{\circ}[/tex]  and [tex]\angle \text{VUW}=(4x+6)^{\circ}[/tex]

To find: Measure of WUT

Solution: Consider the figure in the attached pic.

We know that the angle bisector will divide the angle into two equal halves.

So, we have [tex]\angle \text{WUT}=\angle \text{VUW}[/tex]

Here, [tex]\angle \text{WUT}=(6x-10)^{\circ}[/tex] , and [tex]\angle \text{VUW}=(4x+6)^{\circ}[/tex]

So, we have

[tex]6x-10=4x+6[/tex]

[tex]6x-4x=10+6[/tex]

[tex]2x=16[/tex]

[tex]x=8[/tex]

So, [tex]\angle \text{WUT}=(6x-10)^{\circ}=6\times8-10=38^{\circ}[/tex]

Hence, [tex]\angle \text{WUT}=38^{\circ}[/tex]

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