Why do we define our axes to be perpendicular to each other?

Geometry Level 2

What could have happened if we redefined planar coordinate geometry with our axes to be inclined at an angle other than $\frac{\pi}{2}$ ?

This problem is inspired by megh choksi

The axes would have projections on each other and would not be independent. It would not be a consistent idea because the points on the plane would not have unique coordinates. Nothing at all. We just define it to be

\frac{\pi}{2}

to keep things simple. We'd have a new kind of geometry with new sorts of theorems.