Question

Helpp me asapp with this problem plss will crown brainiest !!!!

Answer 1

Answer:

see below

Step-by-step explanation:

Since RT bisects QRS

1/2  QRS = TRS

1/2 ( 9x+214) = -9x+53

Multiply each side by 2

9x +214 = -18x+ 106

Add 18x from each side

9x +214+18x = 106

27x +214 = 106

Subtract 214 from each side

27x = 106-214

27x =-108

Divide by 27

27x/27 = -108/27

x = -4

TRS = -9x+53

     =-9 *-4 +53

     = 36+ 53

    =89

Answer 2

Answer:

x is -4.

TRS is 89.

Step-by-step explanation:

So we know that QR bisects QRS. By the definition of an angle bisector, this means that the adjacent angles are equivalent. In other words:

$\angle QRT=\angle TRS$

We are told that QRS is (9x+214). QRS is the sum of QRT and TRS. Thus:

$\angle QRS=\angle QRT+\angle TRS$

And since we now that QRT and TRS are equivalent, substitute:

$\angle QRS=\angle TRS+\angle TRS$

Combine like terms:

$\angle QRS=2\angle TRS$

Substitute them for their equations:

$9x+214=2(-9x+53)$

Now, solve for x. On the right, distribute:

$9x+214=-18x+106$

Add 18x to both sides:

$27x+214=106$

Subtract 214 from both sides:

$27x=-108$

Divide both sides by 27:

$x=-4$

So, the value of x is -4.

To find TRS, substitute x=-4 back into the equation. So:

$\angle TRS=(-9(4))+53$

Multiply and add:

$\angle TRS=36+53=89\textdegree$

And we're done!