#### Answer

x=50
y=20
The angles measure 80, 100 and 80.

#### Work Step by Step

Use the definition of a linear pair and substitution to write and solve equations.
Solve for x.
$4y+2x=180\longrightarrow$ a linear pair is supplementary
$2x=180-4y\longrightarrow$ subtraction property of equality
$x=90-2y\longrightarrow$ division property of equality
Solve for y.
$2x+(x+y+10)=180\longrightarrow$ a linear pair is supplementary
$3x+y+10=180\longrightarrow$ combine like terms
$3(90-2y)+y+10=180\longrightarrow$ substitute for x
$270-6y+y+10=180\longrightarrow$ distributive property
$280-5y=180\longrightarrow$ combine like terms
$-5y=-100\longrightarrow$ subtration property of equality
$y=20\longrightarrow$ division property of equality
Substitute to find x.
$x=90-2y=90-2(20)=90-40=50$
Substitute to find the measure of each angle.
$4y=4(20)=80$
$2x=2(50)=100$
$x+y+10=50+20+10=80$