Supplementary Angles

Author

Eric W. Weisstein
August 14, 2026

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

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

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

Illustration

The adjacent angles alpha and beta together form the straight angle AOC.

Module[{angleColor, mark, neutral, origin, phi}, 
  origin = {0, 0}; phi = 2*(Pi/5); angleColor = RGBColor[0.15, 0.45, 0.8]; 
   neutral = LightDarkSwitched[Black, White]; mark[angles_] := 
    {Directive[angleColor, Opacity[0.2]], Disk[origin, 0.6, angles], 
     Directive[angleColor, AbsoluteThickness[2.5]], Circle[origin, 0.6, angles]}; 
   Graphics[{mark[{0, phi}], mark[{phi, Pi}], Directive[neutral, Opacity[1], AbsoluteThickness[2]], 
     Line[{{-1.9, 0}, {1.9, 0}}], Line[{origin, 1.9*{Cos[phi], Sin[phi]}}], PointSize[0.018], 
     Point[origin], Text[Style["α", 18, angleColor, FontFamily -> "Times"], 
      0.83*{Cos[phi/2], Sin[phi/2]}], Text[Style["β", 18, angleColor, FontFamily -> "Times"], 
      0.83*{Cos[(phi + Pi)/2], Sin[(phi + Pi)/2]}], 
     Text[Style["A", 16, neutral, FontFamily -> "Times", FontSlant -> "Italic"], {2.08, 0}], 
     Text[Style["B", 16, neutral, FontFamily -> "Times", FontSlant -> "Italic"], 
      2.05*{Cos[phi], Sin[phi]}], Text[Style["C", 16, neutral, FontFamily -> "Times", 
       FontSlant -> "Italic"], {-2.08, 0}], Text[Style["O", 16, neutral, FontFamily -> "Times", 
       FontSlant -> "Italic"], {0, -0.18}]}]]