Which effect activates first if Number 57 Tri-Head Dust Dragon is summoned while an opponent Slifer the Sky Dragon is on the field in Yu-Gi-Oh?

Answer 1

The turn player has "priority" of effects to be activated first, but in the event that two Trigger effects are activated simultaneously, as in this case, they are put on the Chain in the following order: Turn player's mandatory effects, opponent's mandatory effects, turn player's optional effects, opponent's optional effects. So, technically, they activate simultaneously, but when they are put upon the Chain, they resolve in reverse order of when they are put on.

In short, Number 57's effect resolves first.