When introducting the metric system, the French tried to decimalise the degrees used for angles. They defined the right angle to contain 100 gradians.
Why was the right angle chosen? A somewhat equivalent question: Out of all possible angles, why is the right angle particularly special?
The only idea that comes to my mind is that the right angle is the "average" angle, in the sense that it is the arithmetic mean of all angles between 0 degrees and 180 degrees. A problem with this explanation is that an angle is something that can be an arbitrary number of degrees: it certainly does make sense to talk about 321 degrees, as well as minus 123 (-123) degrees. One can argue that any talk of such angles can be paraphrased into talk of an angle in the interval [0,180] degrees. If my argument holds, the right angle is therefore the "average", "quintessential" angle.
I will probably not accept an explanation along the lines of: "Well, it is called right...". Such an explanation is as good as saying that the golden ratio is of utmost importance in mathematics, which is not the case.
