Exterior Angles of a Polygon and other shapes

I find some students like to memorise this, or at least the first two or three rows and then remember that we keep adding 180 for extra size.

Reason being – an extra triangle.

I feel that using exterior angles is more satisfying.  I find myself walking around an imaginary hexagon in my classroom with arm out stretched.

Here is a very nice Geogebra visualisation of this:

Exterior Angle Collections: REVAMPED! Modify at https://t.co/zXdRkaQEym @geogebra @panlepan @solvemymaths @giohio @gogeometry @NCTM #MTBoS pic.twitter.com/1dgxkNwhgh

— Tim Brzezinski (@dynamic_math) July 16, 2017

And here’s an activity which reinforces this idea.  Use a pencil as an arrow.  Does it always rotate through 360?  Does it always turn the same direction?  Use algebra, maybe?