They equal zero.
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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!
If by "opposite" you mean "additive inverse", the sum is zero. For example, 5 + (-5) = 0.
zero pair
This is not the case. The word opposite can be defined many ways mathematically, but generally indicates either the additive or multiplicative inverse. In most cases, opposite is defined as the addictive inverse. Thus, the sum of a number and its opposite is 0, based on the definition of opposite.
The sum of a number and its negative (additive inverse) is zero. For any nonzero value n, n + (-n) = 0