There are 109 such pairs - unless you don't want to count the combinations of the same numbers but in different order (e.g. 50 + 60 and 60 + 50) - then there are 55 such pairs (up to 55 + 55).
You can also count 0 - sometimes we treat it as a whole number, sometimes we don't - then add two pairs (0 + 110 and 110 + 0) to the 109 pairs result, or 1 pair for 55 pairs result.
