Prompted by the question, "How to denote angle?," I am interested to learn when students consider and reason with angles $> 180^\circ$. For example, when do they reason with an angle of $270^\circ$ representing three Cartesian quadrants? Perhaps this varies from country to country? The issue arises because, e.g., protractors only measure angles in $[0^\circ,180^\circ]$. And the notation $\angle ABC$ seems to mean—at least in certain contexts—the $\le 180^\circ$ angle defined by the two segments $AB$ and $BC$.

My own teaching has been primarily at the US college- and graduate-school levels, where angles $> 180^\circ$ are pretty much taken for granted.

Prompted by the question, "How to denote angle?," I am interested to learn when students consider and reason with angles $> 180^\circ$. For example, when do they reason with an angle of $270^\circ$ representing three Cartesian quadrants? Perhaps this varies from country to country? The issue arises because, e.g., protractors only measure angles in $[0^\circ,180^\circ]$. And the notation $\angle ABC$ seems to mean—at least in certain contexts—the $\le 180^\circ$ angle defined by the two segments $AB$ and $BC$.

My own teaching has been primarily at the US college- and graduate-school levels, where angles $> 180^\circ$ are pretty much taken for granted.