Since the angle which splits a square in a half, starting from it's bottom left corner, is $45^\circ$, I intuitively thought that, if I put two squares to be horizontally adjacent, the angle between the bottom side of the resulting rectangle and the line going from it's bottom left vertex to it's top right vertex would be $22.5^\circ$. My (flawed) reasoning was that it does "half the vertical space a $45^\circ$ angle does". It looks like it's not though, as it's somewhere around $27^\circ$.
I'm sorry if it's a lame question, but why is that? And does that angle have an exact value that we can mathematically derive?