Green’s Dictionary of Slang

cheek v.1

[cheek n.2 (1)]

[mid-19C+] to address in an impudent or insolent manner.

In phrases

cheek it (out) (v.)

[mid–late 19C] to face down, to brazen out.

cheek it through (v.)

[late 19C] (US campus) to assume an air of (spurious) confidence.