Angles Greater than 360 Degrees
Date: 01/01/99 at 09:41:21 From: Queenie Subject: Angles -- Reflex, obtuse or acute? Hi Dr. Math, I know that a reflex angle measures between 180-360 degrees, an obtuse angle measures from 90-180 degrees, and an acute angle measures less than 90 degrees. My question is, what is an angle that measures 425 degrees? My class had a debate. Some people said that it should be a reflex angle because it's greater than 180 degrees, but some people said that it should be an acute angle because it went all the way around and over lapped, leaving an acute angle. I think I'm in for the acute angle, because when you draw an angle, to indicate that the angle is 425 degrees instead of 65, you would have to draw the little arch all the way around and then end it. It looks quite weird. I'm just asking you to make sure. Thanks for your time, looking forward to your reply! :-) -Queenie
Date: 01/03/99 at 18:45:45 From: Doctor Pat Subject: Re: Angles -- Reflex, obtuse or acute? Queenie, 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 http://mathforum.org/dr.math/
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