Complementary Angles

Author

Eric W. Weisstein
August 14, 2026

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

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

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

Illustration

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

Module[{angleColor,mark,neutral,origin,phi},origin={0,0};phi=(π/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,(π/2)}],Directive[neutral,Opacity[1],AbsoluteThickness[2]],Line[{origin,{1.9,0}}],Line[{origin,1.9 {Cos[phi],Sin[phi]}}],Line[{origin,{0,1.9}}],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[(1/2) (phi+(π/2))],Sin[(1/2) (phi+(π/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"],{0,2.08}],Text[Style["O",16,neutral,FontFamily->"Times",FontSlant->"Italic"],{-0.15,-0.15}]}]]