Answer:
x = 65; y = 10
Explanation:
Theorem:
If two parallel lines are cut by a transversal, then same-side interior angles are supplementary.
The three lines are given as parallel, angles 60 deg and (2x - y) deg are supplementary, and angles (2x + y) deg and 40 deg are supplementary. The sum of the measures of supplementary angles is 180. That allows us to write two equations.
2x - y + 60 = 180
2x + y + 40 = 180
Now we simplify the 2 equations.
2x - y = 120
2x + y = 140
Since -y and y are opposites, we can add the equations to eliminate variable y.
4x = 260
x = 65
Now we substitute 65 for x in the first equation of the system of equations and solve for x.
2x - y = 120
2(65) - y = 120
130 - y = 120
-y = -10
y = 10
Answer: x = 65; y = 10