There's some angle of rotation that moves A to where B is now.
What if you did the SAME rotation again ?
It would move A to where C is now.
And what if you did the same rotation a third time ?
It would move A right back to where it is now, and
B and C would also be in their original positions,
just like the picture looks now.
Three rotations bring everything back to its original position.
But that's the same as rotating it all the way around once, and
THAT's 360 degrees.
So each partial rotation must be 1/3 of 360 = 120 degrees.
