Taking the 20th and 21st centuries, the following years have the same day/date combination as 2010:
1909, 1915, 1926, 1937, 1943, 1954, 1965, 1971, 1982, 1993, 1999, 2010, 2021, 2027, 2038, 2049, 2055, 2066, 2077, 2083, 2094 and 2100.
Yes, the year 2094 will have the same day-date selection as 2010.
The 1982 Calendar appears to be the same as 2010.
The next year that has the same day-date combination as 2011 is 2022.
There are 365 days in the year 2010. Therefore, the 364th day of the year is December 30, 2010.
Its the same as all western countries. 1st of January. For 2010 it falls on a friday.
A coincidence
The most recent year with the same day-date correlation as 1980 was 2008. The next year with the same day-date correlation as 1980 will be 2036.
That date can be interpreted in two ways. The 7th of February 2010 was the 38th day of the year and it was a Sunday. July the 2nd 2010 was the 183rd day of the year and it was a Friday.
Prior to 2011, the last year with the same day-date arrangement was 2005. After 2011, the next one will be in 2022.
The question makes no sense since 2010 is not a leap year.
1981
2036