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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.

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    $\begingroup$ A beginning answer: reflex angles were in our Year 8 (13-year-olds) curriculum here in South Australia. $\endgroup$
    – DavidButlerUofA
    Commented Dec 15, 2016 at 0:35
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    $\begingroup$ Although my students up to 6th grade don't work with angles greater than 180 degrees, they are introduced to the 360 degree angle of a circle as young as 4th grade. $\endgroup$
    – Amy B
    Commented Dec 18, 2016 at 15:07

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Students are introduced to reflex angles in primary school in Colorado. However, they use them very little. I teach grades 7-12, and in the Common Core State Standards there are very few standards (if any) that require the use of reflex angles. So, you are correct that just about every student in the U.S. that sees the $\angle{ABC}$ will take that to mean the angle $\angle{ABC}$ that is $\le180$.

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    $\begingroup$ I second this, I also teach 7-12 in a CCSS state and in our state specific-standards (not the general ones, not sure about those..) there is NO mention of angles over 180. I know that specifically at our school students will learn about reflex angles in precalculus and calculus, so usually between 11th-12th grade. Some students never make it to calculus though. $\endgroup$
    – celeriko
    Commented Dec 16, 2016 at 14:09
  • $\begingroup$ "just about every student in the U.S. that sees the ∠ABC will take that to mean the angle ∠ABC that is ≤180" - doesn't this also hold true for the vast majority of professionals dealing with angles for both theoretical and practical work? $\endgroup$
    – yoniLavi
    Commented Dec 17, 2016 at 9:07
  • $\begingroup$ @yoniLavi Yes, I would say so. $\endgroup$
    – MathGuy
    Commented Dec 19, 2016 at 4:09
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My wife uses Singapore Math curriculum. She says angles larger than $180^o$ appear in the 4th grade curriculum. In second grade they see right angles. In third grade they see acute angles and obtuse angles.

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