Defining Exterior Angles of Polygons
Date: 06/24/2004 at 12:47:10 From: Jeri Subject: exterior angles of triangle --What is the anterior angle?? I am having a discussion with my math teacher. He thought the sum of the exterior angles of a triangle was 900 (360*3 - 180). I showed him that the sum is actually 360. However, he said he must have been thinking of the anterior angles. What is an anterior angle? Please help! Thanks!
Date: 06/24/2004 at 13:21:37 From: Doctor Peterson Subject: Re: exterior angles of triangle --What is the anterior angle?? Hi, Jeri. I've never heard of an anterior angle, and don't find that phrase used anywhere on the web along with "polygon". But I have often wondered if there is a name for the entire angle on the outside of a polygon, and have felt uncomfortable calling the supplement of the interior angle the exterior angle when it seems so much more natural to use that name for the "explement" (outside) of the interior angle. Now I know why. Searching the web for such names, I found that although most sites give the definition you and I know for "exterior angle", at least two call the whole outer angle "exterior": Polygon Properties http://www.math.com/tables/geometry/polygons.htm This site defines 'exterior angle' as the angle formed by two adjacent sides outside the polygon. Exterior Angle http://mathworld.wolfram.com/ExteriorAngle.html An exterior angle b of a polygon is the angle formed externally between two adjacent sides. It is therefore equal to 2pi - a, where a is the corresponding internal angle between two adjacent sides. Pictures on both pages make it clear what they mean. The latter page goes on to say Confusingly, a bisector of an angle c is known as an exterior angle bisector, while a bisector of an angle b (which is simply a line oriented in the opposite direction as the interior angle bisector) is not given any special name. This latter term agrees with the familiar definition of exterior angle, rather than with the definition he gives, and may either be the origin of the common usage at lower levels, or a result of confusion over it. So we seem to have different definitions for the same word in different mathematical circles, but some leakage between the two. Your teacher's comment, and my uneasiness, are two instances of interference between the two worlds. Bottom line: be sure you know what definition someone is using before you use the word! If you have any further questions, feel free to write back. - Doctor Peterson, The Math Forum http://mathforum.org/dr.math/
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