What does it mean to have a negative angle?
Negative angles has to do with the direction of rotation that you consider in order to measure angles.
Normally you start counting your angles from the positive side of the x axis in an anti-clockwise direction of rotation:
You can also go clockwise and so to avoid confusion you use a negative sign to indicate this kind of rotation.
We need to remember first that negative has nothing to do with the size of something, just the direction it goes in.
I explain that best by talking about calling your parents for a ride. when they ask how to get to you you can't say I'm 5 miles from home, pick me up! you have to use words like east west left or right. negative is the equivalent of these words in math.
I can walk positive 10 feet or negative 10 feet along the x axis. Same distance, different directions. a positive angle starts from an initial side and moves clockwise to its terminal side. A negative angle starts from an initial side and moves counterclockwise to its terminal side.