Since, PS and QR are parallel, we know that <QRP is equal to <RPS. Therefore, we can solve for y by setting the two equations equal to each other.
5y+14=8y-13
*Subtract 5y from both sides to isolate the variable*
14=3y-13
*Add 13 to both sides*
27=3y
*Divide both sides by 3*
9=y
Now, plug in 9 for y in the equation 8y-13 to find the measure of that angle.
8(9)-13
<RPS=59
Now, the sum of the angles in any triangle is equal to 180 degrees. We can use this knowledge to set up an equation to solve for x.
3x+2x+1+59=180
*Combine like terms*
5x+60=180
*Subtract 60 from both sides*
5x=120
*Divide both sides by 5*
x=24
Now, we can find <RSP by pluggin 24 in for x.
2(24)+1
48+1
<RSP=49 degrees
Hope this helps!!