complementary angles sums up to 90 degrees 1:9 is the division of the total angle that is 90 degrees.
So the sum of ratios 1+9-10
Dividing total angle by total ratio:
90/10 9
Now its clear that each single ratio contains 9 degrees.
so 1:9 means 9 x 1: 9 x 9
which means: 9:81