## Geometry: Common Core (15th Edition)

The Vertical Angle Theorem tells us that $y=2x$. Use the definition of a linear pair and substitution to write and solve equations. Solve for x. $y+(x+y+5)=180\longrightarrow$ a linear pair is supplementary $2x+x+2x+5=180\longrightarrow$ substitute $5x+5=180\longrightarrow$ combine like terms $5x=175\longrightarrow$ subtraction property of equality $x=35\longrightarrow$ division property of equality Solve for y. $y=2x=2(35)=70$ Substitute to find the measure of each angle. $y=70$ $x+y+5=35+70+5=110$ $2x=2(35)=70$