Start by finding x. Look at the second parallel line; you have a straight line that is made up of a 90 degree angle, 2x, and x.
Since a straight line is 180 degrees, and you know a part of it is already 90 degrees, you can make 2x and x add up to 90 degrees.
2x + x = 90, combine like terms.
3x = 90, divide both sides by 3.
x = 30
Find y next. 2y and x are on opposite sides of the transversal and make a Z shape, so they must be alternate interior angles. The alternate interior angle theorem states that these types of angles are congruent.
We know what x is, 30 degrees, so make 2y and x equal to each other.
2y = 30, divide both sides by 2.
y = 15
Find z. Same thing as the bottom parallel line; 2y and z make up the straight line so they must add up to 180 degrees. We found y was 15, so multiply y by 2. y = 30, so make 30 + z add up to 180 degrees.
30 + z = 180, subtract 30 from both sides.
x = 150
