Nobody decided that a right angle was 90 degrees. The concept of 90 degrees was named “right angle.” It is what it is. I suppose there could be a calculus in which a circle is 720 degrees. Far out.

Are you asking why the word “right” is used to describe it, or why it’s divided up into 90 degrees? I think it’s the latter. That was thanks to the Babylonians, who divided up a circle into 360 degrees. It was the ability to divide up 360 lots of different ways that they liked. The 90 degree thing was just a side effect.

The Babylonains divided the circle into 360 degrees. Apart for the divisibility reasons stated, I suspect that the year having 365 days is not a complete coincidence.

No, but it flies with circles. If your circle was 12 inches around, would it fly that the diameter was 3.81972… inches? Of course, if your diameter is one inch, it doesn’t help that there are an integer number of degrees in a circle when your circumference is 3.141592… inches.

Irrational numbers are a fact of life with circles. Might as well make that plainly obvious with 2*pi radians, and simplify all the math while you’re at it.

A lot of geometry would get screwed up if there were no 90 degree angles.

Equilateral, Isosceles and Scalene triangles. Acute, Obtuse and Right triangles. We studied those for weeks. There’s always 180 degrees in any triangle.