  The article analyzes the arguments that became the basis for declaring in
1995, at the 20th General Conference on Weights and Measures that the plane and
solid angles are dimensionless derived quantities in the International System
of Units. The inconsistency of these arguments is shown. It is found that a
plane angle is not a derived quantity in the SI, and its unit, the radian, is
not a derived unit. A solid angle is the derived quantity of a plane angle, but
not a length. Its unit, the steradian, is a coherent derived unit of the
radian.
