Interior Angle

Author

Eric W. Weisstein
August 12, 2026

This notebook downloaded from https://mathworld.wolfram.com/notebooks/Trigonometry/InteriorAngle.nb.

For more information, see Eric's MathWorld entry https://mathworld.wolfram.com/InteriorAngle.html.

©2026 Wolfram Research, Inc. except for portions noted otherwise

Illustration

The highlighted angle lies inside the polygon between the two sides incident to the selected vertex.

Module[{angleColor, neutral, polygon, vertex}, 
  polygon = {{-1.5, 0}, {-0.7, 1.2}, {0.7, 1.2}, {1.5, 0}, {0, -0.8}}; vertex = Last[polygon]; 
   angleColor = RGBColor[0.15, 0.45, 0.8]; neutral = LightDarkSwitched[Black, White]; 
   Graphics[{{Directive[angleColor, Opacity[0.28]], Disk[vertex, 0.55, {0.49, Pi - 0.49}]}, 
     Directive[angleColor, Opacity[1], AbsoluteThickness[2.5]], 
     Circle[vertex, 0.55, {0.49, Pi - 0.49}], Directive[neutral, AbsoluteThickness[2]], 
     Line[Append[polygon, First[polygon]]], Text[Style["θ", 18, angleColor, 
       FontFamily -> "Times"], vertex + {0, 0.78}]}]]