We characterize the trade-off regions between the sum of degrees of freedom (sum-DoF) and feedback delay of channel state information at transmitter (CSIT) in both a X channel and three-user interference channel with local CSIT. As a part of the characterization of the trade-off regions, we demonstrate that the optimal sum-DoF is attainable in the X channel with local and delayed CSIT, provided that CSI feedback is moderately-delayed. Further, we show that it is possible to obtain a higher sum-DoF in the three-user interference channel even with local and moderately-delayed CSIT. A major implication of our work reveals that local and moderately-delayed CSIT is useful to obtain strictly better the sum-DoF over the case no CSIT in a certain class of interference networks.