To solve the equations:

1) (1-x)-1/9=2/9
First, simplify the left side of the equation:
1-x-1/9 = 2/9
x = 1 - 2/9 + 1/9
x = 1 - 1/9
x = 8/9

2) (5-x)+2 1/6=5 5/6
First, convert the mixed number to an improper fraction:
2 1/6 = 13/6

Now simplify the equation:
5 - x + 13/6 = 35/6
-x + 13/6 = 35/6 - 5
-x + 13/6 = 5/6
-x = 5/6 - 13/6
-x = -8/6
x = 4/3

3) (8-x) - 3 2/15 = 2
Convert the mixed number to an improper fraction:
3 2/15 = 47/15

Simplify the equation:
8 - x - 47/15 = 2
-x - 47/15 = 2 - 8
-x - 47/15 = -6
-x = -6 + 47/15
-x = -90/15 + 47/15
-x = -43/15
x = 43/15

So, the solutions to the equations are:
1) x = 8/9
2) x = 4/3
3) x = 43/15