let one angle be x
let the other be y
then their complements are 90-x and 90-y
and their supplements: 180-x and 180-y
(90-x)/(90-y) = 3/4
270 - 3y = 360 - 4x
4x - 3y = 90 , #1
(180-x)/(180-y) = 9/10
1620 - 9y = 1800 - 10x
10x - 9y = 180 , #2
#1 times 3
12x - 9y = 270
2x = 90
x = 45
180 - 3y = 90
-3y = -90
y = 30
so one angle is 45° and the other is 30°
their complements are 45 and 60
45 : 60 = 3:4
their supplements are 135 and 150
135:150 = 9:10
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