Mangement rhymes with:
arrangement, estrangement, rearrangement, arrangement, estrangement, infringement, rearrangement, abridgement, acknowledgement, acknowledgment, arrangement, discouragement, disengagement, disgorgement, encouragement, engagement, enlargement, estrangement, infringement, judgement, judgment, management, micromanagement, misjudgment, mismanagement, nonmanagement, prejudgment, rearrangement, telemanagement
Mangement sounds like:
machined, magenta, maginot, magnant, magnate, magnet, magneti, magnetite, magnitude, maisonet, management, mankind, masonite, massenet, mazzanti, mccamant, mcconathy, mcentee, mcginnity, mcginty, mcintee, mckeand, mcmath, mcnatt, mcnett, mcnitt, mcnutt, migent, mincemeat, miscount, monsanto, monzonite, musante, myoscint