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ktreyb
5y + 14 and 8y -13 we can set equal to each other because they are adjacent angles. 5y + 14 = 8y -13, we are going to subtract 5y from both sides to get 14 = 3y -13. Now add 13 to both sides and get 3y = 27. Divide by 3, y = 9. 

Plug in 9 for 8y - 13 we get 8(9)-13 = 72- 13 = 59. 

The inside angles of triangles must equal 180 so now we have 3x + 2x + 1 + 59 = 180. Combine like terms you get 5x + 60 = 180. Subtract 60 from both sides, you get 5x = 120. Divide by 5, x = 24. This is NOT your answer; we are not done yet!

We must plug in again for the angle represented by 2x + 1. The middle letter tells you which one to plug in for (rSp). x = 24 so 2(24) + 1. 48 + 1 = 49.

Your answer is B. 49. degrees.
abidemiokin

Option B is correct. The measure of m<RSP  is 49 degrees

From the diagram shown

3x + 2x + 1 + 8y - 13 = 180

5x + 8y - 12 = 180

5x + 8y = 180  + 12

5x + 8y = 192 ................. 1

Also, since PQ is parallel to PS, hence;

5y +14 = 8y - 13 (alternate interior angle)

5y - 8y = -13 - 14

-3y = -27

y = 27/3

y = 9

Substitute y = 9 into equation 1

5x + 8y = 192

5x + 8(9) = 192

5x + 72 = 192

5x = 192 - 72

5x = 120

x = 120/5

x = 24

Get the measure of <RSP

m<RSP = 2x + 1

m<RSP = 2(24) + 1

m<RSP = 48 + 1

m<RSP  = 49degrees

Hence the measure of m<RSP  is 49 degrees

Learn more here: https://brainly.com/question/20348771

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