Definition of archly adverb from the Oxford Advanced Learner's Dictionary

 

archly

 adverb
adverb
BrE BrE//ˈɑːtʃli//
 
; NAmE NAmE//ˈɑːrtʃli//
 
(often disapproving)
 
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in an amused way because you know more about a situation than other people ‘Guess what?’ she said archly.