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

step-by-step explanation:

when rotating a figure 180 degrees, imagine that you are able to take the figure and turn it clockwise or counterclockwise around a center point. to rotate a figure 180 degrees, you will need to apply the rule (x, y) → (-x, -y). start by using a coordinate grid with coordinates for each vertex of the figure. the center point of the coordinate grid is located at (0, 0), which is what you will rotate the figure around. write down the original coordinates of the shape you are going to rotate. then, apply the rule. for example, coordinate (1, 2) becomes (-1, -2). another example would be, coordinate (-4, -2) becoming (4, 2). after you change each original coordinate to the rotated coordinate, you will draw your new figure.

step-by-step explanation: