>>Coming here, I remember training myself into these units of measure, to the extent that I tried to remember what were the units for phases of the Moon... and then I remembered that there aren't any.
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>Many of my in-laws spend much time with orienteering, and they use compasses where a full circle is 400­° in stead of 360°, so you never really know what comes next. Maybe a metric calendar?

That'd be grads. I remember a few pocket calculators from late '70s which had an option to work in degrees, radians and grads. Though this is the first time I heard someone is really using them.

Since radians are the only measure which makes sense (mathematically), any other measure is quite arbitrary. So having a right angle of 100 somethings instead of 90 something-elses is at least a way to get rid of them pesky angular minutes and seconds.