Answer:
40 degrees.
Step-by-step explanation:
Because segment PQ and segment PS are perpendicular, the angle they form is a right angle; a 90 degree angle.
We are trying to add angle QPR to angle RPS. They are complementary angles, since they form a 90 degree right angle.
(7x - 9) + (4x + 22) = 90
7x + 4x - 9 + 22 = 90
11x + 13 = 90
11x = 77
x = 7
Since x = 7 and angle QPR is 7x - 9, we can solve for its measure.
7 * 7 - 9 = 49 - 9 = 40.
Angle QPR measures 40 degrees.
Hope this helps!
