Question

Yes,I need help with another one of these , the number that got cut off is 24 btw.

Answer 1

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!!