I don't understand how this equation calculates angle for hexagons....

Hi, I'm learning how to program and I've been studying graphics.

This quote from a programmer confuses me (the quote is a hyperlink to my source):

How does 2pi/n calculate the angle of two vertices relative to the center of a hexagon? I try to plug in some values to test it and the resulting angle is 1.047 degrees which is extremely small and I think I'm misunderstanding the answer.

I have a diagram in my book that also states that the above equation is the angle. I also tested my code (the angle is only a small part of it) and my drawHexagon app works. However, when I do the math, the angle from the center of the hexagon is always 1.047 degrees and that doesn't make sense to me.

Shouldn't the central angle be 60 degrees given that a hexagon has 6 sides?