Answer:
x = 17 and y = 8
Step-by-step explanation:
Since (6x + 3) and (8x - 31) are alternate interior angles, they are congruent.
Therefore, you can set them equal to each other and solve for x.
8x - 31 = 6x + 3
Combine like terms
2x = 34
Divide both sides by two
x = 17
Since (5y + 35) and (6x + 3) are consecutive interior angles, they add up to 180. Plug in 17 for x.
(5y + 35) + (6(17) + 3) = 180
Add like terms
5y + 140 = 180
5y = 40
y = 8
Given: lines l and m are parallel, and line t is a transversal.
angle pair result/justification
1 and 2 are equal (vertical angles)
6 and 8 are equal (corresponding angles)
1 and 4 are equal (alternate exterior angles)
4 and 8 are supplementary angles (i.e. add up to 180 degrees, a straight angle)
Note:
alternate angles are on opposite sides of the transversal, and each attached to a different (parallel) line.
If they are both enclosed by the parallel lines, they are alternate interior angles (examples: angles 2 and 3, 6 and 7)
If they are both outside of the two parallel lines, they are alternate exterior angles (examples: angles 1 and 4, 5 and 8)
Answer:

Step-by-step explanation:
distribute 2 into (4x+2) and -12 into (x-1)
8x+4=4x-12x+12
combine like terms
8x+4=-8x+12
add -8x on both sides
8x+8x+4=12
16x+4=12
subtract 4 on both sides
16x=8
divide both sides by 16
x=1/2
hope this helps
-12 < -6x
-12/-6 > x divide both sides by -6
12/6 > x two negatives makes a positive
2 > x simplify
x < 2 switch sides
hope this helps, God bless!