Editing Angle (section)

=== Common angles and units of measurement ===
{{Multiple image
|perrow = 2/3
|align=right
|direction=horizontal
|image1=Angle obtuse acute straight.svg
|width1=200
|caption1=Acute (<var>a</var>), obtuse (<var>b</var>), and straight (<var>c</var>) angles. All acute and obtuse angles are also oblique angles.

|image2=Zero angle.svg
|width2=81
|caption2=Zero angle

|image3=Right angle.svg
|width3=111
|caption3=[[Right angle]]

|image4=Reflex angle.svg
|width4=81
|caption4=Reflex angle

|image5=Full angle.svg
|width5=81
|caption5=Full angle
}}
Angles are measured in various units, the most common being the [[Degree (angle)|degree]] (denoted by the symbol '''°'''), [[radian]] (denoted by symbol '''rad''') and [[Turn (angle)|turn]]. These units differ in the way they divide up a ''full angle'', an angle where one ray, initially congruent to the other, performs a compete rotation about the vertex to return back to its starting position.

Degrees and turns are defined directly with reference to a full angle, which measures 1 turn or 360'''°'''. A measure in turns gives an angle's size as a proportion of a full angle and a degree can be considered as a subdivision of a turn. Radians are not defined directly in relation to a full angle (see {{Section link|2=Measuring angles|nopage=Y}}), but in such a way that its measure is <math>2\pi</math> rad, approximately 6.28 rad.

There is some common terminology for angles, whose conventional measure is always non-negative (see ''{{section link|#Signed angles}}''):
* An angle equal to 0° or not turned is called a ''zero angle''.{{sfn|Moser|1971|p=41}}
* An angle smaller than a right angle (less than 90°) is called an ''acute angle''{{sfn|Godfrey|Siddons|1919|p=9}} ("acute" meaning "[[Sharpness (visual)|sharp]]").
* An angle equal to {{sfrac|4}}&nbsp;[[Turn (angle)|turn]] (90° or {{sfrac|{{math|π}}|2}} [[radian]]s) is called a ''[[right angle]]''. Two lines that form a right angle are said to be ''[[normal (geometry)|normal]]'', ''[[orthogonality|orthogonal]]'', or ''[[perpendicular]]''.{{sfn|Moser|1971|p=71}}
* An angle larger than a right angle and smaller than a straight angle (between 90° and 180°) is called an ''obtuse angle''{{sfn|Godfrey|Siddons|1919|p=9}} ("obtuse" meaning "blunt").
* An angle equal to {{sfrac|2}}&nbsp;turn (180° or {{math|π}} radians) is called a ''straight angle''.{{sfn|Moser|1971|p=41}}
* An angle larger than a straight angle but less than 1&nbsp;turn (between 180° and 360°) is called a ''reflex angle''.
* An angle equal to 1 turn (360° or 2{{math|π}} radians) is called a ''full angle'', ''complete angle'', ''round angle'' or ''perigon''.
* An angle that is not a multiple of a right angle is called an ''oblique angle''.

The names, intervals, and measuring units are shown in the table below:

{|class = wikitable style="text-align:center;"
|style = "background:#f2f2f2; text-align:center;" | Name&nbsp;&nbsp;
|style = "width:3em;" | zero angle
|style = "width:3em;" | acute angle
|style = "width:3em;" | right angle
|style = "width:3em;" | obtuse angle
|style = "width:3em;" | straight angle
|style = "width:3em;" | reflex angle
|style = "width:3em;" | full angle
|-
! Unit !! colspan=10 | [[Interval (mathematics)|Interval]]
|-
|style = "background:#f2f2f2; text-align:center;" | [[Turn (geometry)|turn]]&nbsp;&nbsp;
|style = "width:3em;" | {{nowrap|0 turn}}
|style = "width:3em;" | {{nowrap|(0, {{sfrac|1|4}}) turn}}
|style = "width:3em;" | {{nowrap|{{sfrac|1|4}} turn}}
|style = "width:3em;" | {{nowrap|({{sfrac|1|4}}, {{sfrac|1|2}}) turn}}
|style = "width:3em;" | {{nowrap|{{sfrac|1|2}} turn}}
|style = "width:3em;" | {{nowrap|({{sfrac|1|2}}, 1) turn}}
|style = "width:3em;" | {{nowrap|1 turn}}
|-
|style = "background:#f2f2f2; text-align:center;" | [[radian]]
| {{nowrap|0 rad}}
| {{nowrap|(0, {{sfrac|1|2}}''{{pi}}'') rad}}
| {{nowrap|{{sfrac|1|2}}''{{pi}}'' rad}}
| {{nowrap|({{sfrac|1|2}}''{{pi}}'', ''{{pi}}'') rad}}
| {{nowrap|''{{pi}}'' rad}}
| {{nowrap|(''{{pi}}'', 2''{{pi}}'') rad}}
| {{nowrap|2''{{pi}}'' rad}}
|-
|style = "background:#f2f2f2; text-align:center;" | [[Degree (angle)|degree]]&nbsp;&nbsp;
|style = "width:3em;" | 0°
|style = "width:3em;" | (0,&nbsp;90)°
|style = "width:3em;" | 90°
|style = "width:3em;" | (90,&nbsp;180)°
|style = "width:3em;" | 180°
|style = "width:3em;" | (180,&nbsp;360)°
|style = "width:3em;" | 360°
|-
|style = "background:#f2f2f2; text-align:center;" | [[Gradian|gon]]&nbsp;&nbsp;
|style = "width:3em;" | 0<sup>g</sup>
|style = "width:3em;" | (0,&nbsp;100)<sup>g</sup>
|style = "width:3em;" | 100<sup>g</sup>
|style = "width:3em;" | (100,&nbsp;200)<sup>g</sup>
|style = "width:3em;" | 200<sup>g</sup>
|style = "width:3em;" | (200,&nbsp;400)<sup>g</sup>
|style = "width:3em;" | 400<sup>g</sup>
|-
|}