Governor's Palace and Mosque
Citadel, Amman, Jordan
This view looking north shows the domed entrance (vestibule) to the Umayyad governor's palace (8th century) in the background. The dome is a modern reconstruction that gives the building an odd, Pac-Man-like appearance. The entrance to the vestibule is the large semicircular archway below the dome. In the foreground are the remains of the palace mosque, whose column bases surround an open courtyard. A short section of the mosque's wall has been reerected here.
The photo makes it clear that the axis of the vestibule is not aligned with the axis of the mosque, which nominally points in the direction of Mecca. There doesn't seem to be any obvious reason why the vestibule could not have been lined up with the mosque, although I suppose there is no architectural rule that would have required it to do so.