Geometry: Common Core (15th Edition)

a) x=64, y=40 b) the angle measures are: $2x=2(64)=128$ $3y=3(40)=120$ $y+20=40+20=60$ $x-12=64-12=52$
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