PLEASE HELP. WILL MARK BRAINLIEST TO THE PERSON WITH THE BEST ANSWER. PLEASE SHOW FULL SOLUTIONS. As shown in the diagram, the lines through points P and Q, and through points R and S are parallel. A transversal intersects the parallel lines at the point P and S, respectively, such that ⦣QPS=(2k+89)° and ⦣PSR=(3k+61)°. Find the measure of ⦣QPS and ⦣PSR in degrees. THANK YOU VERY MUCH AND GOD BLESS.

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  ∠QPS = 101°

  ∠PSR = 79°

Step-by-step explanation:

The marked angles are called "same-side interior angles" or "consecutive interior angles". By either name, they are supplementary.

  (2k +89) +(3k +61) = 180

  5k +150 = 180 . . . . . . . . . collect terms

  5k = 30 . . . . . . . . . subtract 150

  k = 6 . . . . . . . divide by 5

Then the angles are ...

  ∠QPS = (2·6 +89)° = 101°

  ∠PSR = (3·6 +61)° = 79°

∠QPS = 2 x 6 + 89 =101°

∠PSR = 3 x 6 + 61 =79°

Step-by-step explanation:

∠QPS and ∠PSR are consecutive interior angles, they are supplementary

(2k+89) + (3k+61) = 180

5k + 150 = 180

5k = 180-150 = 30

k = 6

∠QPS = 2 x 6 + 89 =101

∠PSR = 3 x 6 + 61 =79