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A. Set up an equation(s) to find x and y.
B. Show all work and solve for x and y.
C. Use these values to find the values of angles 1, 2, and 3.

A Set up an equations to find x and y B Show all work and solve for x and y C Use these values to find the values of angles 1 2 and 3 class=

Respuesta :

A. The equations are given as follows:

  • 12x - 9y = 177.
  • x + 2y = 1.

B. The solutions are given as follows: x = 11, y = -5.

C. The angles are given as follows:

  • m < 1: 57º.
  • m < 2: 57º.
  • m <  3: 123º.

How to obtain the mesures?

The two parallel lines, p and q, are cut by the transversal line, hence angles 2 and 3 are supplementary angles, and thus:

x - 9y + 1 + 11x + 2 = 180

12x - 9y = 177.

Angles 1 and 2 are alternate interior angles, meaning that they are congruent, hence:

6x + y - 4 = x - 9y + 1.

5x + 10y = 5.

x + 2y = 1.

x = 1 - 2y.

Replacing in the first equation, the value of y is given by:

12(1 - 2y) - 9y = 177

33y = -165

y = -165/33

y = -5.


Then the value of x is of:

x = 1 - 2y = 1 + 10 = 11.

The angle measures are given as follows:

  • m < 1: 6(11) - 5 - 4 = 57º.
  • m < 2: 57º -> congruent to 1.
  • m <  3: 123º -> supplementary to 2.

More can be learned about parallel and transversal lines and angles at https://brainly.com/question/24607467

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