Slanted Bridges and String Dynamics

This is a 1.5167 minute video response from DJ Phillips on Sep 15th, 2009

Question:

"When a string is fretted at half of it's length, the pitch goes up one octave. I've noticed that the bridge on most guitars is set at a slight angle, making the lower pitched strings run a slightly longer distance from the nut to the bridge. That means the 12th fret (which runs parallel to the nut) can't be exactly at the halfway point of each string. Why is the bridge set at an angle - and how can the octaves (or other notes for that matter) be in tune with each other?"