Dr. Math's Response to the Great Debate!

Sometimes when debating subjects in math, it is good to consult an expert or two....Her is what Dr. Math had to say about this debat.

http://mathforum.org/library/drmath/view/55067.html

In mathematics we usually separate angles into "angles of inclination" 
and "angles of rotation." If you use the basic ideas of geometry in a 
plane, an angle is the "opening" between two rays. This leads to the 
names above. But if we talk about angles greater than 360 degrees, this 
can not happen "between" two rays. I have never heard anyone give 
either of the names to angles greater than 360 because we almost always 
are talking about the rotation of an angle in terms of some reference 
or stationary ray. Perhaps a more important term would be the term used 
in expressing the idea you gave when you wrote "because when you draw 
an angle, to indicate that the angle is 425 degrees instead of 65" is 
the word COTERMINAL. Mathematically we would say a 425 degree rotation 
is coterminal with a 65 degree rotation, and both are coterminal with 
a negative 295 degree rotation.  

Although I would not say a 425 degree angle is "acute," I would say it 
had an acute "reference angle." The purpose of the language is to help 
us understand the things which are alike, and those which are 
different, so to me, it wouldn't be accurate to just say a 425 degree 
angle is acute.  

Hope this helps.

- Doctor Pat, The Math Forum