Question

Y'all I really need some help here. 100 points.

Answer 1

42 Degrees

Step-by-step explanation

Becuase (11x-27) and (9x+3) are vertical angles that means they are equal to each other

(11x - 27) = (9x + 3)

First you will add 27 to both sides

11x -27 = 9x +3

+27 +27

Making it to:

11x = 9x + 30

Now you need to subtract 9x from both sides

11x = 9x +30

-9x -9x

Turning it into this

2x= 30

Now Lastly, divide both sides by 2

2x = 30

2x 2x

And the answer is...... X=15

Now that you have the x value, we go back to the 11x-27 and replace the X with 15

11(15) -27 = 138 degress

Now because angle QUT and 138 degrees make a straight line that means together they will be 180 degress so you will subtract 180 by 138

Giving you the final answer of

42 Degrees

Answer 2

42 degrees

Explanation:

So, first to find <QUT, which is a vertical angle, we have to figure out either QUR or TUS. So:

9x+3=11x-27

solve for x:

x=15

Then, plug it into one of the equations. Let's use 9x+3.

9(15)+3=138

So, we know that QUR is 138 degrees.

That means that TUS is ALSO 138.

138x2=276

Now we know that QUT and RUS have to equal whatever 360-276 is:

360-276=84

QUT and RUS have to equal 84 degrees, so we DIVIDE by 2.

84/2=42

So, QUT=42 degrees