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Because the opposite of 8 for example is -8 and 8+(-8) = 0
The sum of a number and its opposite would be zero. Example: 8 + -8 (since it's easier to not use double signs i'll write it this way) 8 - 8 = 0.
If the opposite is meant to be the additive opposite and not the multiplicative opposite, then their sum is zero. The reason is that is what defines an additive opposite!
The sum of 8 and 2 is 10
If by "opposite" you mean "additive inverse", the sum is zero. For example, 5 + (-5) = 0.