Complementary angles are sets of angles (2 angles) whose angles sum to 90 degrees. So let's write a formula for each scenario.
1) We'll call one angle x. So we know the other angle is 'twice as large' so it must be 2x. We also know that they must sum to 90 degrees, so
x + 2x = 90
Solving for x, we get x = 30. So one angle is 30 degrees, the other is 60 degrees.
2) We'll call the first angle x again. The other angle is '8 times as large', so it must be 8x. Therefore,
x + 8x = 90
Solving for x, we get x = 10. Thus, one angle is 10 degrees, the other is 80 degrees.
Hope this helps!
