2hinge verb
hinges; hinged; hing·ing [+ obj] : to attach (a door, gate, or cover) by hinges — usually used as (be) hinged ▪ a storage trunk with a hinged lid
hinge on also hinge upon [phrasal verb]
hinge on/upon (something) : to be determined or decided by (something) : to depend on (something)
▪ The outcome of the election hinges on how the candidates perform in the debate.
▪ The outcome of the election hinges on how the candidates perform in the debate.
