If angles were metric, which do you prefer?

[Last Hussar]

If they made geometry metric, which do you think they should go for?
A circle is 100 degrees, instead of 360.
A right angle is 100, instead of 90?

[Lord Kermit of Birkenhead]

Cept that metric angles are in mils 6400 to a circle

[Last Hussar]

 

[Raider4]

A right angle is 100, instead of 90?

Gradians. 

[Last Hussar]

Today I learned...

[d_Guy]

Now try metric angels.

[steve_holmes_11]

The thing about the SI / Metric systems is that they start with three chosen values (Mass, distance, time).
All others are derived as formulae based on those.

Speed is distance / time.
Volume is distance * distance * distance.
etc.

An angular value that fits the system would use some kind of ratio.
I know of two.

Radians: 
Imagine a cheese "triangle" where the distance arounf the arc is the same as a straight side.
The angle between the two straight sides is a radian.
Radians are great for maths, orbital mechanics and some other physics.
It's very difficult to eyeball an angle and estimate in radians.
Radians would also be useless for navigation or surveying - none of the useful angles shake out to whole numbers.

Mils (Milliradians):
Shooters use these on optical gunsights.
One milliradian represents one metre sideways at a kilometer range.
Mils are great for extremely long thin triangles (Like leading a moving target with your 17pdr).
We're talking minutes of arc rather than degrees.
The nice linear maths stops mathing at almost any significant angle - leaving you a hostage to trigonometry.
20th century naval gunnery, or shooting at aircraft require different solutions.

Gradians are a decent hack for people raised on degrees.