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PolygonAngle—Wolfram Language Documentation

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• See Also
  • PlanarAngle
  • DihedralAngle
  • SolidAngle
  • VectorAngle
  • PolyhedronAngle
  • Polygon
  • GeometricScene
• Related Guides
  • Region Properties and Measures
  • Synthetic Geometry
  • Plane Geometry
  • Angles and Polar Coordinates

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 p_i of poly in canonical form Polygon[{p₁,…,p_n},data].

• 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.

The list of angles at the vertex points:

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

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

The interior angle of a polygon at the vertex points:

The exterior angle of a polygon at the vertex points:

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

The sum of interior angles of a regular polygon is :

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

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