Algebra applications: find the value of x and y

x = 65; y = 10

Step-by-step 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

x = 65; y = 10

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