Answer:
m∠SQT = 142° ,
m∠PQS = m∠SQT = 71°
m∠TQR = 41°
Step-by-step explanation:
For better understanding of the solution, see the figure which is attached below :
Given : Ray QS bisects the angle PQT
⇒ m∠PQS = m∠SQT
Now, m∠PQT = m∠PQS + m∠SQT
9·x + 34 = 2 × m∠SQT
4.5·x + 17 = 8·x - 25
⇒ 3.5·x = 42
⇒ x = 12
Therefore, m∠SQT = 142° ,
m∠PQS = m∠SQT = 71°
Now, m∠SQR = 112°
⇒ m∠TQR = m∠SQR - m∠SQT
= 112° - 71°
= 41°
