Here's why:
* Open syllable: A syllable that ends with a vowel sound.
* Closed syllable: A syllable that ends with a consonant sound.
The word "investigate" has the following syllables:
* In - Closed syllable (ends with consonant sound "n")
* Ves - Closed syllable (ends with consonant sound "s")
* Ti - Open syllable (ends with vowel sound "i")
* Gate - Closed syllable (ends with consonant sound "t")
Therefore, while it has one open syllable ("ti"), it's not an open syllable word overall.