m∠RSU = (5x+7) ° and m∠UST = (9x-1) °. If ∠RSU and ∠UST are complementary, what is the measure of each angle?

37° and 53° respectively.

Step-by-step explanation:

We need to know that the angles are complementtary if ∠RSU + ∠UST = 90°. Then,

5x+7 + 9x-1 = 90

5x + 9x + 7 - 1 = 90

14x + 6 = 90

14x = 90 - 6

14x = 84

x = 84/14

x = 6.

Then, the angle ∠RSU has measure 5 (6) + 7 = 30+7 = 37, and the angle ∠UST has measure 9 (6) - 1 = 54-1 = 53.