# How to denote angle?

I'm teaching mathematics on my free time for young pupils. Once I have seen that they denote angles like $\angle ABC$. But sometimes I have difficulties to understand whether they mean an angle or its explementary angle, especially in problems containing angles in a circle. Should I worry about this or should I teach them some other notation, like $\angle ABC$ is the explementary angle of $\angle CBA$ or the $\angle ABC$ where the some given point $D$ is between the rays $BA$ and $BC$? And also if some most talented pupils wants to participate in mathematics competitions, should he or she write the answers so that one knows exactly which angle he or she means or is it better to save a few seconds just by leaving the reader to think which one angle he or she means?

• Interpreting $\angle ABC$ as the counterclockwise angle that maps $BC$ to $AC$ is an important convention. With that (or the opposite) convention, the ambiguity is removed. – Joseph O'Rourke Dec 11 '16 at 22:23
• @JosephO'Rourke, in the elementary school where I taught, the books teach that $\angle ABC$, is equivalent to $\angle CBA$. Either way the angle always stands for the angle that is 180 degrees or less. Not sure where this convention came from, but it is clearly different than your convention. – Amy B Dec 12 '16 at 14:23
• @AmyB: Maybe my convention comes later in the educational pipeline, fitting in with the right-hand-rule for e.g. cross-products. – Joseph O'Rourke Dec 12 '16 at 14:58
• @JosephO'Rourke Considering that the OP is teaching "young pupils", the ordinary convention for the Euclidean program (ie, the protractor postulate) of measuring angles from 0 to 180 degrees is appropriate here. I have never encountered a counterclockwise convention in any school geometry textbook or competition. Also, what do you mean that an angle "maps" $BC$ to $AC$? – Andrew Dec 14 '16 at 18:31
• @Andrew: Oops, typo. Maps $BC$ to $BA$ = rotates $BC$ about $B$ counterclockwise, until it lies along $BA$. – Joseph O'Rourke Dec 14 '16 at 20:29