Physics Projectile Motion Question (Part 2)?

[celestial ninja]

For a projectile that lands at the same level from which it starts, state another launch angle above the horizontal that would result in the same range as a projectile launched at an angle of 36, 16 and 45.6 degrees. Air resistance is negligible.

**since all the sin ratios are positive, I figured that I could just draw the initial angle of 36 degrees, and then subtract 36 from 180....but that's not getting the right answer
In my textbook, they have subtracted all of the above degree values from 90 degrees, to get the answer....but I don't understand why....
Can anyone explain to me why ? Thanks very much in advance!!