Adjacent Angles

Author

Eric W. Weisstein
August 12, 2026

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

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

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

Illustration

The two highlighted angles share a vertex and a side, and their interiors are disjoint.

Module[{angleColor, mark, neutral, origin, rays}, 
  origin = {0, 0}; rays = {0, 0.8, 1.75}; angleColor = RGBColor[0.15, 0.45, 0.8]; 
   neutral = LightDarkSwitched[Black, White]; mark[angles_, color_] := 
    {Directive[color, Opacity[0.2]], Disk[origin, 0.6, angles], 
     Directive[color, AbsoluteThickness[2.5]], Circle[origin, 0.6, angles]}; 
   Graphics[{mark[rays[[{1, 2}]], angleColor], mark[rays[[{2, 3}]], angleColor], 
     Directive[neutral, Opacity[1], AbsoluteThickness[2]], 
     (Line[{origin, 1.9*{Cos[#1], Sin[#1]}}] & ) /@ rays, PointSize[0.018], Point[origin], 
     Text[Style["α", 18, angleColor, FontFamily -> "Times"], 0.83*{Cos[0.4], Sin[0.4]}], 
     Text[Style["β", 18, angleColor, FontFamily -> "Times"], 0.83*{Cos[1.275], Sin[1.275]}], 
     Text[Style["O", 16, neutral, FontFamily -> "Times", FontSlant -> "Italic"], {-0.18, 0.12}]}]]