Call the angle x.

The supplement of x is 180 - x.

The compliment of x is 90 - x.

So, the supplement is 6 times as large as the compliment:

180 - x = 6(90 - x)

180 - x = 540 - 6x

5x = 360

x = 72

90 - x = 18

180 - x = 108

(All the previous angles are measured in degrees, of course.)

-Dan