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Wiktionary
answerphone

n. (context British NZ English) A telephone containing a built-in device for recording incoming callers’ messages for later retrieval.

Wikipedia
Answerphone (song)

"Answerphone" is the debut single by Scottish singer Nicholas McDonald, who finished as the runner-up on the tenth series of The X Factor in 2013. It was written by McDonald alongside Paul Barry. It was released on 16 March 2014 as the lead single from McDonald's debut studio album In the Arms of an Angel (2014). The song peaked at number 73 on the UK Singles Chart and number 28 on the Scottish Singles Chart.

Usage examples of "answerphone".

Smith with his answerphone and presumably an automatic bleeper to alert him to messages so that he was always the one to phone you.

He dialed the number Kusum had left on the office answerphone yesterday.