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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.....

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 thro class=

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sqdancefan

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Answer:

  ∠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°

Answer:

∠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

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