Final answer:
To find the measure of angle SQR, use the fact that angles SQP and PQR are supplementary. Set up an equation and solve for x, then plug in the value of x to find the measure of angle SQR.
Step-by-step explanation:
To find the measure of angle SQR, we can set up an equation using the given information. Since angle SQP and angle PQR are supplementary angles, their measures add up to 180 degrees. So we have: m < SQP + m < PQR = 180 degrees.
Substituting the given values, we have: 5x + 34 = 180.
Now we can solve for x: 5x = 180 - 34 = 146, so x = 146/5. Plug in this value of x to find the measure of angle SQR: m < SQR = 3(146/5) - 2 = 438/5 - 2 = 438/5 - 10/5 = 428/5 = 85.6 degrees.