The phrase "gat the measure of" means to understand someone's strengths and weaknesses or to have a confident understanding of someone or something. There are several synonyms for this phrase that can be used to convey the same meaning. Some of these synonyms include 'size up,' 'assess,' 'appraise,' 'evaluate,' 'estimate,' 'judge,' 'weigh,' and 'meet and match.' These words can be used interchangeably to imply that an individual has formed a deep insight into something or someone by evaluating them closely. The choice of words depends on the specific context in which they are used, but all of them carry the meaning of getting a good understanding of someone or something.