Final answer:
Leap years occur every four years to align the calendar year with the astronomical year. While 1992, 2004, 1964, 1852, and 1788 were leap years, 1800 was not because it was a century year that was not divisible by 400, according to the rules of the Gregorian calendar.
Step-by-step explanation:
A leap year occurs roughly every four years to correct the discrepancy between the calendar year and the tropical year. The years 1992 and 2004 are leap years and are divisible by 4, indicating they follow the basic leap year rule. However, under the Gregorian calendar, which is the calendar system used today, there's an additional rule for century years (years ending in two zeros). A century year must be divisible by 400 to be a leap year.
Was 1964 a leap year? Yes, because it is evenly divisible by 4. Was 1852 a leap year? Yes, it was, as it also is divisible by 4 and falls before the more specific rule on century years being only leap years if divisible by 400. Was 1788 a leap year? Again, yes, because it is divisible by 4.
The reason 1800 was not a leap year is that, while it is divisible by 4, it is a century year that is not divisible by 400. This exception to the rule helps align the calendar year with the astronomical year more closely.