Replacing a tyre

[raleighnut]

I've never heard the 90⁰ before and have always done 180⁰.

That makes it more difficult to get the last bit on as you're 'fighting' the valve (it won't allow the bead to drop into the rim centre well) at least with the 1/4 turn (90 degrees) the part of the tyre opposite is able to drop into the centre more easily

 

[Ajax Bay]

I'm in the @raleighnut school but go for the 270 option. Care with the valve first, then avoid the 'beads won't go into the well by the valve' issue with 180.
With 270, the beads at 90 can go deep into the well.
The very idea of thumbing the final bead over the rim by the valve (and maybe pushing the valve up with the third hand) ensures avoidance, also for many decades.

 

[Ian H]

With wide tyres it doesn't matter. For narrow tyres valve last is easier, sometimes critically so if it's a 'difficult' tyre.