Explanation:
when 2 lines intersect, then the 2 angles on top are the same as the 2 angles below the intersection - just left-right mirrored.
and the sum of both intersection angles on one side of a line are together 180° (because one side of such a line is representing a half-circle around the intersection point).
and when parallel lines are intersected by the same line, then all 4 angles at one intersection point are the same as the 4 angles at the other intersection points. otherwise the lines are not parallel.
so,
angle 1 = angle 4 = angle 5 = angle 8
angle 2 = angle 3 = angle 6 = angle 7
angle 1 + angle 2 = angle 2 + angle 4 =
= angle 3 + angle 4 =
= angle 3 + angle 1 = 180°
angle 5 + angle 6 = angle 6 + angle 8 =
= angle 8 + angle 7 =
= angle 7 + angle 5 = 180°
we know angle 7 = 75°.
therefore,
angle 2 = angle 3 = angle 6 = 75°
therefore,
3x -18 = 75
3x = 93
x = 31
angle 4 + angle 3 = angle 4 + 75 = 180°
angle 4 = 105°
y + 25 = 105
y = 80