A female gametophyte of an angiospermic plant is developed from a...

The megaspore mother cell (MMC) in the ovule undergoes one meiotic division to produce four haploid megaspores.

Out of these four megaspores, usually three degenerate and only one remains functional.

The functional megaspore then undergoes three successive free-nuclear mitotic divisions.

The first mitotic division produces a $2$-nucleate stage, the second produces a $4$-nucleate stage, and the third produces an $8$-nucleate stage.

These $8$ nuclei eventually organize into the typical $7$-celled, $8$-nucleate female gametophyte (embryo sac).

Thus, the entire process requires one meiotic division and three mitotic divisions.

Answer: one meiotic and three mitotic divisions