Final answer:
The moon phase 1 month before a waxing gibbous is a waning gibbous, and 1 month after is a waning crescent. This is due to the moon's approximately 29.5-day cycle completing a full rotation and nearly starting over.
Step-by-step explanation:
The moon phase that occurs 1 month before a waxing gibbous is the waning gibbous, and the moon phase 1 month after a waxing gibbous is the waning crescent. Since the moon cycle lasts about 29.5 days, we conclude that the moon phase a month before or after any given phase will be the same phase since it will have completed a full cycle plus approximately two extra days. When considering the waxing gibbous phase, which occurs after the first quarter and before the full moon, a full lunar cycle before this phase would be in a similar waxing gibbous phase, and a full lunar cycle after would return to a similar waxing gibbous phase, albeit slightly earlier in the moon's cycle due to the roughly one-month (29.5 day) period.