Here, the sentence talks about the 'teacher' as general class of people like 'Arnold'. Since we are referring to general things, we need to use the definite article 'a/an'. The word 'American' starts with a vowel and therefore 'an' will be used.
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Q. Idioms and phrases for - To live in clover
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Q. . . . . . . . . teachers of this school are very liberal and intelligent.
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