Geometry: Angles and Triangles

[iluvgreen7]

Please help

Line segment RS intersects line segment LM at P, the measure of angle RPL=4x+y, measure of angle LPS=28x-14, measure of angle MPS=x+10y
a)solve for x and y
b) Find the measure of angle RPL, the measure of angle LPS and the measure of angle MPS

How do i solve for both x and y

 

[Bob Brown MSEE]

Part A: Use opposite angles

angle MPS = angle RPL
Eqaution #1) x + 10 y = 4 x + y

If angles are in degrees
180 = angle MPS + angle LPS
180 = x + 10 y + 28 x - 14
Equation #2) 180 = 29 x + 10y - 14

Use two equations with two unknowns to get x and y.