As an aside to above discussion (which is a perfect explaination of the systems itself) the 90 degrees comes from an aircraft design perspective rather than the pitot static design.
For a given distance out from the aircraft skin the shortest distance to the aircraft would be 90 degree angle, so less material in the design and less instrument in the airstream, overall less drag. Moving inside the aircraft if the tube comes into the aircraft other than perpendicular you need to add more weight to the system to get it to point towards where you would like it, adding more tubes etc.
The effect of the above is small, but when it comes to the crunch every little helps. Flattening the rivet heads on a Spitfire increased it's top speed by 10mph and I have worked on modern fighter aircraft where we have scolloped around fasteners to save fractions of a pound in weight.