Step 1: Frame acute angle closure glaucoma as a pressure emergency where speed of pressure reduction decides the choice.
Step 2: Therapy begins systemically. An osmotic such as IV mannitol draws water out of the vitreous and lowers pressure quickly, and IV acetazolamide cuts aqueous formation. Mannitol gives the most rapid drop, so it is started first.
Step 3: Topical agents like pilocarpine and timolol are layered in only after the pressure begins to fall, because at extreme pressures the iris muscle is ischaemic and pilocarpine cannot constrict it effectively. Mydriatics like atropine are contraindicated as they worsen the block.
Step 4: The lasting cure is a peripheral iridotomy done after medical control. As the first line drug among the choices, IV mannitol is correct.
\[\boxed{\text{IV mannitol}}\]