x= 12
PQS= 71º
PQT= 142º
TQR= 41º
First, you need to find x. To do that, you need to form an equation that would look like this:
(PQT)/2=SQT --> (9x+34)/2 = 8x-25
First, simplify the left side.
(9x+34)/2 = 8x-25
4.5+17 = 8x-25
Next, subtract 4.5x from both sides.
4.5x+17 -4.5x =8x-25 -4.5x
17=3.5x+25
Now, add 25 from both sides.
17 +25 =3.5x+25 +25
42=3.5x
Finally, divide both sides by 3.5.
42/3.5 = 3.5x/3.5
12=x
Now that we now x, we can plug x in to get all the measurements.
PQT=
9(12)+34
108+34
142º
PQS=
142/2
71º
TQR=
112-71
41º
Hope this helps!
If you need a larger explanation or if you what like me to help with another question, just let me know :)