The way the angles are listed and the fact that it says line PQ is perpendicular to line PS both suggest that the two angles are complementary. This means their sum adds up to 90 degrees. So...
(7x - 9) + (4x + 22) = 90
Combine like terms:
11x + 13 = 90
Subtract 13 from both sides to isolate the variable and its coefficient:
11x = 77
Divide both sides by 11 to isolate the variable:
x = 77/11
x = 7
Now we plug this into what it's asking for.
QPR = 7x - 9
7(7) - 9
49 - 9
40
m∠QPR should be 40 degrees.