Not only did Joseph Smith claim to be visited by angels but he also claimed to have heard the voices of angels.
Doctrine and Covenants 128:20-21 reads:
And again, what do we hear? Glad tidings from Cumorah! Moroni, an angel from heaven, declaring the fulfilment of the prophets—the book to be revealed. A voice of the Lord in the wilderness of Fayette, Seneca county, declaring the three witnesses to bear record of the book! The voice of Michael on the banks of the Susquehanna, detecting the devil when he appeared as an angel of light! The voice of Peter, James, and John in the wilderness between Harmony, Susquehanna county, and Colesville, Broome county, on the Susquehanna river, declaring themselves as possessing the keys of the kingdom, and of the dispensation of the fulness of times!
And again, the voice of God in the chamber of old Father Whitmer, in Fayette, Seneca county, and at sundry times, and in divers places through all the travels and tribulations of this Church of Jesus Christ of Latter-day Saints! And the voice of Michael, the archangel; the voice of Gabriel, and of Raphael, and of divers angels, from Michael or Adam down to the present time, all declaring their dispensation, their rights, their keys, their honors, their majesty and glory, and the power of their priesthood; giving line upon line, precept upon precept; here a little, and there a little; giving us consolation by holding forth that which is to come, confirming our hope!
What would give Joseph Smith the confidence to claim this if it wasn’t true?