Final answer:
Angle-closure glaucoma is a contraindication to the administration of cholinergic-blocking medications due to the risk of increased intraocular pressure.
Step-by-step explanation:
The finding in a patient's history that would be a contraindication to the administration of a cholinergic-blocking medication is Angle-closure glaucoma. This is because anticholinergic drugs, which block the effects of the neurotransmitter acetylcholine, can potentially increase intraocular pressure, exacerbating glaucoma. Therefore, patients with angle-closure glaucoma should avoid cholinergic-blocking medications as they might worsen their condition.