Ploidy of synergid is

Synergids are haploid because haploid megaspore divides mitotically to produce them.

Megaspore mother cell (2n) undergoes meiosis to give rise to 4 haploid (n) megaspores. Out of four megaspores three degenerstes and one remains functional. Functional megaspore undergoes three times free nuclear mitosis to form 8 nucleated and 7 celled embryosac with wall formation after nuclear divisions.

2 synergids (n)  + 1 central cell (n + n) + 1 egg cell (n) + 3 antipodals (n) = 7 celled and 8 nucleated embryosac