Finding internal angles of polygons using ArcGIS Desktop?

Question

I'm working on ArcMap 10.3.1. I'd like to retrieve the values of all internal angles of each polygon of a shapefile, and return them as follows:

• either concatenated on a new field;
  
• or on a table;
  
• or as a new points shapefile, in which each point corresponds to a vertex of each of the original polygons, with an attribute for "angle".

Whichever way I get the values for the angles is fine.

Answer 1

This will do some work for polygons not sharing edges:

arcpy.FeatureVerticesToPoints_management("PGON", "./vertices.shp", "ALL")
arcpy.DeleteIdentical_management("vertices", "Shape")
arcpy.PolygonToLine_management("PGON", "./singleLine.shp")
arcpy.SplitLine_management("singleLine", "/splits.shp")
arcpy.AddGeometryAttributes_management("splits", "LINE_BEARING")

Name your vertices and assign their names to fromNode and toNode fields in splits and transfer line bearings to vertices table using join with relevant fields. Vertices below are labelled by in/out bearings:

This field calculator expression computes internal angles:

def internalA (fr,to):
 external=180-fr+to
 if external<0:external+=360
 if external>360:external-=360
 return external
 #--------------
internalA ( !fromB!, !toB! )