(a) The director, division of traffic engineering shall determine upon what streets angle parking shall be permitted and shall mark or sign such streets; but such angle parking shall not be indicated upon any federal-aid or state highway within the urban county unless the state highway department has determined that the roadway is of sufficient width to permit angle parking without interfering with the free movement of traffic.
(b) Angle parking shall not be indicated or permitted at any place where passing traffic would thereby be caused or required to drive upon the left side of the street.