For a Gaussian broadcast channel, it is known that: the capacity region in general is enlarged in the presence of feedback from all the receivers; and in the physically degraded case, feedback does not enlarge the capacity region. It is shown that the capacity region of a two-user Gaussian broadcast channel (GBC) is enlarged even when the feedback is available from only one of the receivers. Furthermore, in the degraded case with full feedback, we demonstrate an explicit capacity achieving coding strategy, with the decay of error doubly exponential in the number of transmissions specific to any given message.