Talk:Internal and external angles

Untitled

"The sum of the internal angles of a polygon on a Euclidean plane with n vertices (or equivalently, n sides) is (n − 2)180 degrees."

??? Isn't this true only for CONVEX polygons?

No. --Spoon! 21:14, 23 February 2007 (UTC)[reply]

only if you take the concave angles as negative Cal3000000 (talk) 14:26, 17 June 2024 (UTC)[reply]

description of external angle incorrect, and does not match illustration

definition reads, "..an exterior angle (or external angle) is an angle formed by one side of a simple polygon and a line extended from that side."

An angle formed by a side...and a line extended from that side: now, wouldn't that simply be a continuation of a line and thus form NO angle (or a 180° angle)?

I believe this should read, instead: ..."an exterior angle (or external angle) is an angle formed by one side of a simple polygon and a line extended from an adjoining side. 71.209.40.102 (talk) 01:52, 25 January 2008 (UTC)[reply]

exterior angles part is confusing

I don't get it. If I take, for example, a square (to keep things simple), it has interior angles that are each 90 degrees. From this I intuit that the corresponding exterior angle for each interior angle is 270 degrees, since that is the measure of arc on the outside. This stuff presumes that there is only one exterior angle for each vertex, yet that angle does not cover all of the arc of that exterior side. And if we use an extension of a side to define these exterior angles, then in my drawing there are three exterior angles at each corner. This single exterior angle seems totally arbitrary and defies the beauty of most Euclidean geometry, especially since it is so counterintuitive. 65.80.246.160 (talk) 21:12, 23 March 2010 (UTC)[reply]

Tough. It is not the duty of wikipedia to regulate what maths 'should' be, we just have to describe it as it is. Also, if you think that is counterintuitive, please do not research other maths Cal3000000 (talk) 14:28, 17 June 2024 (UTC)[reply]