Editing Angle (section)

===Polygon-related angles===
[[File:ExternalAngles.svg|thumb|300px|right|Internal and external angles]]
* An angle that is part of a [[simple polygon]] is called an ''[[interior angle]]'' if it lies on the inside of that simple polygon. A simple [[concave polygon]] has at least one interior angle, that is, a reflex angle. {{pb}} <!-- --> In [[Euclidean geometry]], the measures of the interior angles of a [[triangle]] add up to {{math|π}} radians, 180°, or {{sfrac|2}} turn; the measures of the interior angles of a simple [[convex polygon|convex]] [[quadrilateral]] add up to 2{{math|π}} radians, 360°, or 1 turn. In general, the measures of the interior angles of a simple convex [[polygon]] with ''n'' sides add up to (''n''&nbsp;−&nbsp;2){{math|π}}&nbsp;radians, or (''n''&nbsp;−&nbsp;2)180&nbsp;degrees, (''n''&nbsp;−&nbsp;2)2 right angles, or (''n''&nbsp;−&nbsp;2){{sfrac|1|2}}&nbsp;turn.
* The supplement of an interior angle is called an ''[[exterior angle]]''; that is, an interior angle and an exterior angle form a [[#Linear pair of angles|linear pair of angles]]. There are two exterior angles at each vertex of the polygon, each determined by extending one of the two sides of the polygon that meet at the vertex; these two angles are vertical and hence are equal. An exterior angle measures the amount of rotation one must make at a vertex to trace the polygon.{{sfn|Henderson|Taimina|2005|p=104}} If the corresponding interior angle is a reflex angle, the exterior angle should be considered [[Negative number|negative]]. Even in a non-simple polygon, it may be possible to define the exterior angle. Still, one will have to pick an [[orientation (space)|orientation]] of the [[plane (mathematics)|plane]] (or [[surface (mathematics)|surface]]) to decide the sign of the exterior angle measure. {{pb}} <!--
--> In Euclidean geometry, the sum of the exterior angles of a simple convex polygon, if only one of the two exterior angles is assumed at each vertex, will be one full turn (360°). The exterior angle here could be called a ''supplementary exterior angle''. Exterior angles are commonly used in [[Logo (programming language)|Logo Turtle programs]] when drawing regular polygons.
* In a [[triangle]], the [[bisection|bisectors]] of two exterior angles and the bisector of the other interior angle are [[concurrent lines|concurrent]] (meet at a single point).<ref name=Johnson>Johnson, Roger A. ''Advanced Euclidean Geometry'', Dover Publications, 2007.</ref>{{rp|p=149}}
* In a triangle, three intersection points, each of an external angle bisector with the opposite [[extended side]], are [[collinearity|collinear]].<ref name=Johnson/>{{rp|p=149}}
* In a triangle, three intersection points, two between an interior angle bisector and the opposite side, and the third between the other exterior angle bisector and the opposite side extended are collinear.<ref name=Johnson/>{{rp|p=149}}
* Some authors use the name ''exterior angle'' of a simple polygon to mean the ''explement exterior angle'' (''not'' supplement!) of the interior angle.<ref>{{citation|editor=D. Zwillinger|title=CRC Standard Mathematical Tables and Formulae|place=Boca Raton, FL|publisher=CRC Press | year=1995 | page= 270}} as cited in {{MathWorld |urlname=ExteriorAngle |title=Exterior Angle}}</ref> This conflicts with the above usage.