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5) x=32

6) x=86, y=94

7) x=21, y=29.5

Step-by-step explanation:

5) the two angles are considered alternate exterior, so they are congruent.

5x-64=3x, add 64 to the other side and subtract 3x to the other side.

2x=64, divide by 2.

x=32.

6) 86 and y are a linear pair, so set the two equal to 180.

y+86=180, subtract by 86

y=94

Using the consecutive angles theorem, we can determine that the angle that makes a vertical pair with x is also 86. Because vertical pairs are equivalent, x=86.

7) To solve x, set it equal to 59; the two are equivalent according to the Consecutive angles theorem.

3x-4=59, add 4

3x=63, divide by 3

x=21

Because 2y and 59 are a vertical pair, set them equal to each other.

2y=59, divide by 2

y=59/2 or 29.5

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