cheer vs amuse

cheer is a noun but amuse is not a noun.

Word	Noun	Adjective	Verb	Adverb
cheer	Yes	No	Yes	No
amuse	No	No	Yes	No

As verbs, amuse is a hyponym of cheer; that is, amuse is a word with a more specific, narrower meaning than cheer:

cheer (noun)	amuse (noun)
the quality of being cheerful and dispelling gloom
a cry or shout of approval

cheer (verb)	amuse (verb)
become cheerful	make (somebody) laugh
spur on or encourage especially by cheers and shouts	occupy in an agreeable, entertaining or pleasant fashion
show approval or good wishes by shouting
cause (somebody) to feel happier or more cheerful
give encouragement to