#### 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.)
$3x+8=3(14)+8=42+8=50$
$5x-20=5(14)-20=70-20=50$
$5x+4y=5(14)+4(15)=70+60=130$