Answer:
5) x=32
6) x=86, y=94
7) x=21, y=29.5
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