# 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

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## Basic Examples(2)

The list of angles at the vertex points:

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

The angle at the point 1 of in canonical form:

## Scope(6)

### Basic Uses(3)

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

The angle at the vertex point:

PolygonAngle works on polygons:

PolygonAngle works on polygons with GeoGridPosition:

### Specifications(3)

#### "Interior"(1)

The interior angle of a polygon at the vertex points:

#### "Exterior"(1)

The exterior angle of a polygon at the vertex points:

#### "FullExterior"(1)

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

## Properties & Relations(2)

The sum of interior angles of a regular polygon is :

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

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_2024_polygonangle, author="Wolfram Research", title="{PolygonAngle}", year="2019", howpublished="\url{https://reference.wolfram.com/language/ref/PolygonAngle.html}", note=[Accessed: 20-June-2024 ]}

#### BibLaTeX

@online{reference.wolfram_2024_polygonangle, organization={Wolfram Research}, title={PolygonAngle}, year={2019}, url={https://reference.wolfram.com/language/ref/PolygonAngle.html}, note=[Accessed: 20-June-2024 ]}