A seal assembly for a turbomachine is provided. The turbomachine includes a stationary housing and a rotor rotatable about an axis. The seal assembly includes a plurality of arcuate packing ring segments disposed intermediate to the rotor and the stationary housing, and a plurality of inter-segment gaps disposed between the plurality of arcuate packing ring segments. The plurality of inter-segment gaps are inclined at a first angle from a radial axis of the rotor and inclined in a direction of motion of the plurality of arcuate packing ring segments. The seal assembly also includes a biasing member disposed intermediate to the stationary housing and the plurality of arcuate packing ring segments and coupled to both.