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Solve for x and y, then find angle measures:

Solve for x and y, then find angle measures:-example-1

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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

User Yuriy Kravets
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