In which horizontal quarter are the angles 70 degrees 124 degrees 359 degrees -65 degrees -137 degrees.

The logic is extremely simple, we divide the circle into 4 quarters and mark them counterclockwise in the + direction, by simple logical manipulations we get that
70 degrees – 1 quarter, mk from 0 to 90
124 degrees – 2 quarter, mk from 90 to 180
359 degrees – 4 quarter, mk from 270 to 360
-65 degrees – 4 quarter, as we go in the opposite direction and from 0 to -90
-137 degrees – 3 quarter, by analogy with the previous one, from -90 to -180