岂 is literary and formal. In everyday speech, people use 怎么能 (zěnme néng) or 难道 (nándào) instead. You'll encounter 岂 in written Chinese, news, speeches, and set phrases like 岂有此理.
grammar
岂 forms rhetorical questions expecting a negative answer: 岂能 (how could one), 岂不是 (isn't it), 岂有 (how could there be). The pattern 岂不是...吗 is very common.
