Answer: x=10 y=15
Explanation:
You can solve this by creating a system of equations.
(90-4y) = (50-2x) because they are vertical angles
and
(2x+3y)+(x+5y)+(50-2x)=180 because they create a straight line
If we combine all like terms we get two equations
]4y-2x =40
8y + x= 130
We can then solve through either substitution or elimination. Let's do elimination. We'd need to multiply everything in the bottom equation by 2 so that they x's will cancel out:
4y - 2x = 40
16y +2x=260
20y = 300
y = 15
Then we can plut 15 into 4y-2x= 40 to solve for x
4(15) - 2x = 40
x = 10
Then you just plug these x and y values into the equation for each angle. They aren't named, so I'll write the equations
90-4y =30 = 50-2x
2x+3y= 65
x+5y= 85