If QS bisects <PQT, m<SQT = (8x-25)°, m<PQT = (9x+34)°, and m<SQR = 112°, find each measure

Question

If QS bisects <PQT, m<SQT = (8x-25)°, m<PQT = (9x+34)°, and m<SQR = 112°, find each measure

Answer 1

Answer 2

It would be helpful to draw this. But without drawing, since Q is written in the middle of the angles, we know S is sticking out. That means the angles labeled with S (as one of the 3 letters) are the "half" angles. "Bisects" means it cuts the angle into two equal halves. So <PQT = <SQR and <SQT

After substituting:

9x + 34 = 112 + 8x - 25

x + 34 = 87

x = 53

Now substitute 53 for x in the expressions for each angle to solve for each angle.