Solve for the value of y and the measures of angles 1 and 3. Show your work for credit.?

Question

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Answer 1

Simple. Angles 1 and 3 are congruent because they're vertical angles. You know that angle 1 = 6y+29 and angle 3 = 12y-7. If the two angles are equal, then:
6y+29 = 12y-7.
Solve for y:
29 = 12y-6y-7
29 = 6y-7
36 = 6y
6 = y
Now solve for angles 1 and 3. Angle 1 = 6y+29. Substitute the y with 6:
angle 1 = 6(6)+29
angle 1 = 36+29 = 65.
Since angles 1 and 3 are vertical angles, they're congruent and angle 3 also equals 65. To check to make sure, substitute 6 for y in the equation for the measure of angle 3 (12y-7):
angle 3 = 12(6)-7 = 72-7 =65.

Answer 2

angle 1 = angle 3
therefore
6y+29 = 12y - 7
29 + 7 = 12y - 6y
36 = 6y
y = 6

likewise angle 2 = angle 4
therefore
4x +31 = 6x -11
31 + 11 = 6x -4x
42 = 2x
x = 21

to find the angles, just substitute y = 6 into the equations
angle 1 = 6y + 29
= 36 + 29
= 65 degrees.
angle 1 = angle 3 = 65 degrees

Answer 3

m1 + m2 = 180 (supplementary angles)
6y + 29 + 4x + 31 = 180
4x + 6y = 120
2x + 3y = 60 ---- (1)

m3 + m4 = 180 (again, supplementary angles)
12y - 7 + 6x - 11 = 180
6x + 12y = 198
2x + 4y = 66 ---- (2)

(2) - (1): y = 6

Hence,
m1 = 6(6) + 29 = 65 degrees
m3 = 12(6) - 7 = 65 degrees

Also m1 and m3 are opposite angles, and therefore m1 = m3.

Answer 4

y=6 and the two angles are 65 deg each. Since angles 1 and 3 are alternating consecutive angles, they are equal to each other. Setting the equations for them equal and rearranging, one gets 6y+36=12y, from which y=6