Explanation:
it is a bit difficult to read the handwriting (and even the printed original texts) in this diffuse picture.
let's go through the 3 problems as I could decipher them.
1)
from what I can see you made a calculation mistake for y.
but you were right with your approaches.
12x - 8 = 15x - 23
15 = 3x
x = 5
therefore,
12x - 8 = 12×5 - 8 = 60 - 8 = 52°
and the large angle up there is
52 + 70 = 122°
and now
6y + 96 = (12x - 8) + 70 = 122
6y = 26
y = 26/6 = 13/3
by the way, x and y are not angles (and degrees). they are just factors in the expressions to calculate some angles.
12, 15 and 6 are not ° either. all are calculation factors or terms, that then together define the ° of angles.
2)
you made a mistake with the identification of what angles the linear pair is.
3x = 5x - 20
20 = 2x
x = 10 (again, not °, just a number)
3x = 3×10 = 30° (this is then an angle)
= 5x - 20
for y we could then use 2 different approaches
a) your linear pair approach.
4y is one angle, true, but the other is (2y + 3x) !
so,
4y + 2y + 30 = 180
6y = 150
y = 25 (again, not °, just a number)
2y = 50°
4y = 100°
3)
I hope you are right with (11x + 19) and (12y - 24). I would have read this in the picture as (11x + 18). and it could be (12y + 24).
assuming you are right :
11x + 19 = 7x + 47
4x = 28
x = 7 (again, not °, just a number)
11x + 19 = 7x + 47 = 96°
7z + 17 = 87
7z = 70
z = 10 (again, not °, just a number)
and yes, for y we are using the linear pair again. the two combining angles are (12y - 24) and (11x + 19).
(12y - 24) + (11x + 19) = 12y - 24 + 96 = 180
12y + 72 = 180
12y = 108
y = 9 (again, not °, just a number)
12y - 24 = 12×9 - 24 = 108 - 24 = 84°