>The Morley construction is done entirely
>by using angles (input two
>of the angles of the
>scalene triangle, trisect all three
>of these angles, intersect adjacent
>trisectors, etc.) It stands
>to reason that there should
>be enough relationships among these
>angles to provide a proof
>of the theorem. But
>there are not enough pure
>angle relationships to solve for
>all the angles.

In proof #1 at

http://www.cut-the-knot.com/triangle/Morley/

one can replace the last identity for the sides of the equilateral triangle with identities for its angles through the theorem of sines, as one posibility.

In this manner the sides play an auxiliary role, nothing else.

Your question is somewhat ambiguous. Do you consider the law of sines a mixed (side/angle) identity, or an angle identity? If the latter, your question has been answered above. If the former, then you should rethink your question, because specifying the angles fixes the shapes of the triangle and leads to the law of sines.