so...that...如此...以至于...这个句型哪部分是状语,一般都什么状语

so...that...如此...以至于...这个句型哪部分是状语,一般都什么状语
新概念59课最后一句话yesterday my husband removed the gate and Rex got so annoyed that we have not seen him since.课文注释写的句中含有一个so annoyed that...的状语从句.这个句子里哪里是状语,如果that后的是状语,又是什么状语?那这样翻译起来觉得很别扭啊.到底哪部分是状语,修饰的又是谁.that后的部分到底是什么成份?