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?
The answer is:
- You should not worry about it.
- Yes, you should let the reader interpret the angle according to the context.
There is no defined convention for notation of explementary angles. Because it's not of much practical importance. However if you skim through some papers, you'll notice that generally, angles are taken to be the ones less than 180 i.e., unless explementary is explicitly mentioned. In other words explementary angles are often taken to be greater than 180.
Also, when it's imperative to explicate which angle is being referred to, it's better to label the corresponding arc, and mention the angle as the one spanning through the specified arc.