Answer
x=14
y=15
The vertical angles measure 50.
The other angle measures 130.
Work Step by Step
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.)
$3x+8=3(14)+8=42+8=50$
$5x-20=5(14)-20=70-20=50$
$5x+4y=5(14)+4(15)=70+60=130$
