生气 -> 生我的气 . 的 in a certain grammatical structure I came across the following sentence: 如果不是这样的话，那你为什么生我的气

I haven't seen 生气 as a verb before and was confused by the grammar of 生我的气 but didn't know how to google it as I don't even have the language to describe the situation well. Can someone point me in the right direction to this aspect of Chinese grammar? Thanks!
生气 is a verb for "get angry; take offence"

'的' in  生我的气 is an 'adjectival particle' that turns the noun '我'(I) into  '对我的'(toward me) 

'生气' (get angry) --> '生(对)我的(怒)气' = ( 生气 *at me**) = (get angry at me) 

'生气' is a two characters verb, but '气' in '生我的气', is treated as a noun '怒气'

more example:

'发火' (get mad) -->'发不必要的火' = (发 unnecessary 火) = (get mad unnecessarily ) 

'发火' is a two characters verb, but '火' in '发不必要的火' is treated as a noun '怒火'

A more telling example:


  问话 [ask word] = questioning
  
  问你的话 [ask your word] = questioning you
  
  '话' here is treated as a noun 'words' instead of part of the two characters word 问话 (questioning)