# Talk:Exterior angle theorem

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Field: Geometry

What kind of proof is THAT?!? Ok, I recognize it as a psuedo-high school geometry two-column proof, but this is circular. The first reason ("sum... = 180") is a result of the exterior angle theorem. 98.186.83.178 (talk) 17:46, 12 December 2010 (UTC) ccw009@uark.edu

Furthermore (now that I've signed in), half of the "reasons" are omitted! This is pathetic - like my wikiediting abilities, which prevent me from fully revamping this article. 888Xristos (talk) 17:56, 12 December 2010 (UTC)

I agree, when studying triangles, the exterior angle theorem is proved before the interior angle sum theorem. Weimer (talk) 01:58, 25 April 2011 (UTC)

## Massive copyvio

I noticed the large amount of poorly-formatted text on this site, whose style seemed kind of "incongruous" to that of the rest of the page, and decided to do some googling. I discovered it is copied off of: http://www.cut-the-knot.org/fta/Eat/EAT.shtml

From the site:

The Exterior Angle Theorem (Euclid I.16), "In any triangle, if one of the sides is produced, then the exterior angle is greater than either of the interior and opposite angles," is one of the cornerstones of elementary geometry. In many contemporary high-school texts, the Exterior Angle Theorem appears as a corollary of the famous result (equivalent to the Parallel Postulate) that the three angles of a triangle sum to two right angles -- (since adjacent interior and exterior angles are supplementary, the sum of the two remote interior angles equals the exterior angle, which must thus be greater than either one alone). ...

From the article:

The Exterior Angle Theorem (Euclid I.16), "In any triangle, if one of the sides is produced, then the exterior angle is greater than either of the interior and opposite angles," is one of the cornerstones of elementary geometry. In many contemporary high-school texts, the Exterior Angle Theorem appears as a corollary of the famous result (equivalent to the Parallel Postulate) that the three angles of a triangle sum to two right angles -- (since adjacent interior and exterior angles are supplementary, the sum of the two remote interior angles equals the exterior angle, which must thus be greater than either one alone). ...

And it goes on, copying essentially the entirety of the cited page word-for-word. Even the links at the end of the article were copied (albeit in non-functional form)! As the site does not appear to license its content under a compatible Free license (see http://www.cut-the-knot.org/Terms.shtml), I've removed all this text (see WP:COPYVIO). But I would like to supply my own words that would go over the same points, since it did add useful information to the article. The problem, though, is I'm not sure if the given site (which would be an easy-at-hand source for citing) would be an adequate source for Wikipedia's purposes, even though the claims made there are not, I believe, "extraordinary". mike4ty4 (talk) 09:27, 17 August 2013 (UTC)

## The general theorem

According to Richeson, Euler's Gem: The Polyhedron Formula and the Birth of Topology, Princeton (2008), Page 220, the so-called "Exterior angle theorem" states that the exterior angles of any convex polygon sum to 2π.

Are there two "exterior angle theorems" to be disambiguated, or is one of these theorems wrongly named? — Cheers, Steelpillow (Talk) 12:44, 20 February 2015 (UTC)