In this paper, we study frequency-division duplexing (FDD) based cell-free massive multiple-input multiple-output (MIMO) systems wherein distributed multi-antenna access points (APs) serve many single-antenna users simultaneously. Most previous work on cell-free massive MIMO systems consider time-division duplexing mode, although FDD systems dominate current wireless standards. The key challenges in FDD massive MIMO systems are mainly channel-state information (CSI) acquisition and feedback overhead. To address these challenges, we exploit the so-called angle reciprocity of multipath components in the uplink and downlink, so that the required CSI acquisition overhead scales only with the number of served users. We propose a low complexity multipath component estimation technique and present two linear angle-of-arrival (AoA)-based beamforming schemes. We analyze the performance of these schemes by deriving closed-form expressions of the mean-square-error for multipath component estimation, as well as closed form expression for the downlink spectral efficiency. Simulation results demonstrate that the proposed multipath component estimation technique outperforms conventional subspace-based and gradient-descent based techniques. We show also that the proposed beamforming schemes perform close to the ideal beamforming techniques.