Answer
a) x=64, y=40
b) the angle measures are:
$2x=2(64)=128$
$3y=3(40)=120$
$y+20=40+20=60$
$x-12=64-12=52$
Work Step by Step
Postulate 3.1 tells is that when a transverse intersects parallel lines, same-side interior angles are supplementary.
$2x+(x-12)=180\longrightarrow$ write an equation and solve for x
$3x-12=180\longrightarrow$ combine like terms
$3x=192\longrightarrow$ addition property of equality
$x=64\longrightarrow$ division property of equality
$3y+(y+20)=180\longrightarrow$ write an equation and solve for y
$4y+20=180\longrightarrow$ combine like terms
$4y=160\longrightarrow$ subtraction property of equality
$y=40\longrightarrow$ division property of equality
