“意气相投”常见的英文表达有 “be of like mind”、“hit it off” 或 “be in harmony with each other in temperament and interests”。以下是具体解释和例句：
1、 be of like mind
* 含义：指思想、观点、兴趣等一致，即“意气相投”。
* 例句：We are of like mind on many important issues.（我们在许多重要问题上意气相投。）
2、 hit it off
* 含义：指初次见面就相处得很好，有“意气相投”的感觉，常用于描述人与人之间的相处。
* 例句：They hit it off immediately and became good friends.（他们一见如故，很快成了好朋友。）
3、 be in harmony with each other in temperament and interests
* 含义：这是一个较为正式且详细的表达，指在性格和兴趣上彼此和谐一致，即“意气相投”。
* 例句：Despite their different backgrounds, they found they were in harmony with each other in temperament and interests.（尽管他们背景不同，但他们发现彼此在性格和兴趣上意气相投。）