Answer:
x = 100, y = 50
Explanation:
Make a system of equations:
First, you know that x + y degrees and 30 degrees are on a line together, they add up to 180 degrees:
x + y + 30 = 180
x + y = 150
Next, the interior angles of a triangle always add up to 180 degrees, and since 2y, x/2, and 30 are all the angles in a triangle, you have:
2y + x/2 + 30 = 180
x/2 + 2y = 150
Now, all you have to do is solve the system of equations.
To start, multiply the second equation by 2 to get rid of the fraction:
x + 4y = 300
Then, you can subtract the two equations:
x + 4y = 300
- (x + y = 150)
3y = 150
divide both sides by 3
y = 50
substitute y = 50 into the equation x + y = 150:
x + 50 = 150
x = 100