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What do complementary angles mean?

they compliment each other

ah? so one angle says to the other " hey, nice angle" ?

No they both equal to 90 degrees

okay good.

that means they add up to 90 degrees, correct?

yes

right. so let us say one angle is A and the other angle is B

A : B = 1 : 9, right?

right

and A+B = 90. Are you with me?

ya i get you so far

good. so you have two equations
A + B = 90
and
A/B = 1/9

A / B = 1 / 9
=> A = 9B

substitute A in the other equation and solve for B