## Geometry: Common Core (15th Edition)

Use the Vertical Angles Theorem, which tells us that verticals angles have equal measures, to write an equation and solve for x. $3x+8=5x-20$ $3x+28=5x\longrightarrow$ addition property of equality $28=2x\longrightarrow$ subtraction property of equality $14=x\longrightarrow$ division property of equality By definition, linear angles are supplementary. Write an equation and substitute for x to find y. $(3x+8)+(5x+4y)=180$ $8x+8+4y=180\longrightarrow$ combine like terms $8(14)+8+4y=180\longrightarrow$ substitute for x $112+8+4y=180\longrightarrow$ simplify $120+4y=180\longrightarrow$ simplify $4y=60\longrightarrow$ subtraction property of equality $y=15$ Substiute to find the measure of each angle. (The vertical angles have the same measure, so it is only necessary to solve one term.) $3x+8=3(14)+8=42+8=50$ $5x-20=5(14)-20=70-20=50$ $5x+4y=5(14)+4(15)=70+60=130$