It's still perfect since you can just take 32040 of these (= 89*360, ggt is 1 since 89 is prime) and then you will have a full circle. A real shame it would have been when you would have took an irrational amount of degrees since then this calculation would not be possible. There could only be an approximation that makes it impossible in reality to decide if it is right or not but mathematically speaken it would be impossible.