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PolygonAngle[poly]

gives a list of angles at the vertex points of poly.

PolygonAngle[poly,p]

gives the angle at the vertex point p of a polygon poly.

PolygonAngle[poly,i]

gives the angle at the point pi of poly in canonical form Polygon[{p1,…,pn},data].

PolygonAngle[…,"spec"]

gives the angle specified by "spec".

Details
Details and Options Details and Options
Examples  
Basic Examples  
Scope  
Basic Uses  
Specifications  
"Interior"  
"Exterior"  
"FullExterior"  
Properties & Relations  
See Also
Related Guides
History
Cite this Page

PolygonAngle

PolygonAngle[poly]

gives a list of angles at the vertex points of poly.

PolygonAngle[poly,p]

gives the angle at the vertex point p of a polygon poly.

PolygonAngle[poly,i]

gives the angle at the point pi of poly in canonical form Polygon[{p1,…,pn},data].

PolygonAngle[…,"spec"]

gives the angle specified by "spec".

Details

  • PolygonAngle is also known as interior angle.
  • PolygonAngle[poly, p] gives the angle delimited by the two adjacent sides intersecting at p.
  • The following specifications "spec" can be given:
  • "Interior"interior (inside) angle at p
    "Exterior"exterior angle at p
    "FullExterior"full exterior angle at p
  • PolygonAngle[poly,p,"Interior"] is equivalent to PolygonAngle[poly,p].
  • PolygonAngle[poly,p,"Exterior"] is equivalent to π-PolygonAngle[poly,p].
  • PolygonAngle[poly,p,"FullExterior"] is equivalent to 2π-PolygonAngle[poly,p].
  • PolygonAngle can be used with symbolic polygons in GeometricScene.

Examples

open all close all

Basic Examples  (2)

The list of angles at the vertex points:

Wolfram Language code: ℛ = Polygon[{{-1., 0.}, {0., 1.7320508075688772}, {1., 0.}}, {1, 3, 2}];
Wolfram Language code: PolygonAngle[ℛ]

The angle at the vertex point {-2,0}:

Wolfram Language code: ℛ = DynamicModule[«3»];
Wolfram Language code: PolygonAngle[ℛ, {-2, 0}]

The angle at the point 1 of ℛ in canonical form:

Wolfram Language code: PolygonAngle[ℛ, 1]

Scope  (6)

Basic Uses  (3)

Use PolygonAngle to find the list of angles at the vertex points:

Wolfram Language code: ℛ = DynamicModule[«3»];
Wolfram Language code: PolygonAngle[ℛ]

The angle at the vertex point:

Wolfram Language code: PolygonAngle[ℛ, {1., 1.5}]

PolygonAngle works on polygons:

Wolfram Language code: DynamicModule[«3»];
Wolfram Language code: PolygonAngle[%, 1]

Parallelogram:

Wolfram Language code: PolygonAngle[Parallelogram[], 1]

RegularPolygon:

Wolfram Language code: PolygonAngle[RegularPolygon[5], 1]

PolygonAngle works on polygons with GeoGridPosition:

Wolfram Language code: Polygon[GeoGridPosition[{{{-0.9950503945490105, 1.2366760550756015}, {-0.9952074890903578, 1.2369207053693891}, {-0.9952196732768064, 1.2369073327446167}, {-0.9953160063787643, 1.236848436956935}, {-0.9954141759436825, 1.2369993898475449}, {-0. ... 197645333103}, {-0.9949098578570917, 1.2368130881428654}, {-0.9948663952535768, 1.2367477711687371}, {-0.9948714472169538, 1.2367426500757825}, {-0.9949211061652593, 1.2367089232486177}, {-0.9949439717990124, 1.236746107097628}}}, "Bonne"]];
Wolfram Language code: PolygonAngle[%, 1]

Specifications  (3)

"Interior"  (1)

The interior angle of a polygon at the vertex points:

Wolfram Language code: ℛ = DynamicModule[«3»];
Wolfram Language code: PolygonAngle[ℛ, "Interior"]

"Exterior"  (1)

The exterior angle of a polygon at the vertex points:

Wolfram Language code: ℛ = DynamicModule[«3»];
Wolfram Language code: PolygonAngle[ℛ, "Exterior"]

"FullExterior"  (1)

The full exterior angle of a polygon at the vertex points:

Wolfram Language code: ℛ = DynamicModule[«3»];
Wolfram Language code: PolygonAngle[ℛ, "FullExterior"]

Properties & Relations  (2)

The sum of interior angles of a regular polygon is :

Wolfram Language code: Total[PolygonAngle[RegularPolygon[5]]] == 3Pi

PolygonAngle[ℛ, p] is equivalent to PlanarAngle[p->{q1,q2}] where q1 and q2 are adjacent points of p in a polygon ℛ:

Wolfram Language code: ℛ = Polygon[{{1., 0.}, {0.5, 0.8}, {-0.5, 0.8}, {-1., 0.}}]
Wolfram Language code: PolygonAngle[ℛ, {0.5, 0.8}]
Wolfram Language code: PlanarAngle[{0.5, 0.8} -> {{-0.5, 0.8}, {1., 0.}}]
Wolfram Research (2019), PolygonAngle, Wolfram Language function, https://reference.wolfram.com/language/ref/PolygonAngle.html.

Text

Wolfram Research (2019), PolygonAngle, Wolfram Language function, https://reference.wolfram.com/language/ref/PolygonAngle.html.

CMS

Wolfram Language. 2019. "PolygonAngle." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/PolygonAngle.html.

APA

Wolfram Language. (2019). PolygonAngle. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/PolygonAngle.html

BibTeX

@misc{reference.wolfram_2026_polygonangle, author="Wolfram Research", title="{PolygonAngle}", year="2019", howpublished="\url{https://reference.wolfram.com/language/ref/PolygonAngle.html}", note=[Accessed: 12-June-2026]}

BibLaTeX

@online{reference.wolfram_2026_polygonangle, organization={Wolfram Research}, title={PolygonAngle}, year={2019}, url={https://reference.wolfram.com/language/ref/PolygonAngle.html}, note=[Accessed: 12-June-2026]}