Any abilities of the destroyed creatures that trigger when the player is dealt damage won't trigger.

Any abilities that trigger when creatures die while resolving Angrath's last ability won't be put on the stack until after the player is dealt damage. If the player's life total becomes 0 or less, those triggers won't resolve in time to save that player.

Angrath's first and last abilities target only the player. Creatures with hexproof that player controls will be affected.

Angrath's last ability uses the power of those creatures as they last existed on the battlefield to determine their total power. If a creature's power was somehow less than 0, it subtracts from the total power of the other creatures. If the total power of those creatures is 0 or less, Angrath doesn't deal damage.

If a creature controlled by the target opponent isn't destroyed as Angrath's last ability resolves (most likely because it has indestructible), its power still contributes to the amount of damage dealt. Use its power as it currently exists on the battlefield to determine the total power of the creatures.