The past tense of dangle a carrot in front of is dangled a carrot in front of.
The third-person singular simple present indicative form of dangle a carrot in front of is dangles a carrot in front of.
The present participle of dangle a carrot in front of is dangling a carrot in front of.
The past participle of dangle a carrot in front of is dangled a carrot in front of.