Although in effect this
definition of a wide angle
lens works, it isn't entirely
true. As
35mm cameras have become more
ubiquitous and defining of the
photo advertising and
sales industry the
precise definition of what makes a wide angle lens has become less
used.
A wide angle lens is not defined by its angle of view, but rather by its angle of coverage. The angle of view is dictated simply by the focal length of the lens, whereas the angle of coverage is dictated by lens' construction. In effect, a wide angle lens can cover more film than a 'normal' lens of equal focal length. This definition isn't important when one is dealing only with 35mm film, but when one accounts for film format changes this becomes critical because the smaller the focal length of the lens the less coverage a lens offers.
A true wide angle lens should have a covering angle of 80-100 degrees regardless of its focal length. Super-wide angle lenses with coverage of up to 180 degrees have become available in recent years as well. Thus, while the lens would never need to be built it is entirely possible for a 35mm camera to use a wide-angle lens with a focal length of 120mm or whatever one desired. It would be silly, but it could be done.
The main reason it is important to go into this detail is for someone interested in Large Format photography where one is capable of putting pretty much any lens one wants onto a given camera - but they won't all do the job. 90mm 'normal' lenses, 90mm wide angle lenses and 90mm super-wide lenses are available. All three will give the same angle of view on a 4x5" camera, but the 'normal' variety will show vignetting, the wide angle variety will barely allow for movement within the camera and the super-wide will let you get away with just about anything...