Funnily enough the metre is defined by the globe as well: the arc from the equator to North pole is defined as 10,000 km. I think this might be where the alternative angle metrics came from, which went with the metre:

full circle is 400 grad, so a right angle (10,000 km) is 100 grad.

Then minutes and seconds are factors of 100, so a centesimal minute is 1 km and 1 centesimal second is 10 m.