Question

Please help me i dont understand

Answer 1

40 degrees.

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!

Answer 2

∠ QPR = 40°

Explanation:

∠ QPR + ∠ RPS = ∠ QPS, substitute values

7x - 9 + 4x + 22 = 90, that is

11x + 13 = 90 ( subtract 13 from both sides )

11x = 77 ( divide both sides by 11 )

x = 7

Thus

∠ QPR = 7x - 9 = 7(7) - 9 = 49 - 9 = 40°