Answer
$x = 80$ degrees; $y = 50$ degrees
Work Step by Step
The sum of all interior angles in a triangle equals $180$ degrees. Also, adjacent angles on a straight line add up to $180$ degrees as well. This means that we can write the following system of equations: $$x + y + y =180$$ $$(2x - 30) + y = 180$$ which is to say, $$x + 2y = 180$$ $$2x + y = 210$$ We can use the substitution method to solve for one of the variables. Taking the first equation, we get the following: $$x + 2y = 180$$ $$x = 180 - 2y$$ and plug the equivalent value into the other equation: $$2x + y = 210$$ $$2(180 - 2y) + y = 210$$ $$(360 - 4y) + y= 210$$ $$360 - 210 = 3y$$ $$150 = 3y$$ $$50 = y$$ We now substitute this value into the previous equation: $$x = 180 - 2y$$ $$x = 180 - 2(50)$$ $$x = 180 - 100 = 80$$
