Question

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

Answer 1

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°