The point isn't to save us in our sins, but to save us from our sins. That is what we are redeemed, or rather, recovered, from.
Then this amazing verse follows. It states clearly that Christ has power given from the Father to redeem us "because of repentance". That is related to the previous verse. We aren't redeemed in our sins, we are redeemed from them, i.e. we have to change first, and then we can be forgiven through the atonement. We aren't forgiven of things we haven't stopped doing yet. The more we repent and change, the more we can enjoy the cleanliness of forgiveness through the atonement and the more fully we can enjoy the gift of the Holy Ghost. It is by that progression that we are ultimately saved. Those are the conditions, and so angels were sent to declare "the conditions of repentance, which bringeth unto the power of the Redeemer, unto the Salvation of their souls". That power is exercised only to the degree we repent.
11 And he hath power given unto him from the Father to redeem them from their sins because of repentance; therefore he hath sent his angels to declare the tidings of the conditions of repentance, which bringeth unto the power of the Redeemer, unto the salvation of their souls.
If we do not build on Christ, we cannot be saved. He set the perfect example, and we must strive to follow it. I should note that in these days of wickedness, the world has severely distorted what Christ's example was from the way Christ actually behaves in the four gospels, as well as in the other scriptures.
It is also worth noting that we are fooling ourselves if we think we are building on Christ without drinking deeply and freely from the words of those Christ called as his prophets and apostles, as well as the scriptures he has given us. We cannot both build on Christ, and reject Christ's words and priesthood given to lead us back to him.
12 And now, my sons, remember, remember that it is upon the rock of our Redeemer, who is Christ, the Son of God, that ye must build your foundation; that when the devil shall send forth his mighty winds, yea, his shafts in the whirlwind, yea, when all his hail and his mighty storm shall beat upon you, it shall have no power over you to drag you down to the gulf of misery and endless wo, because of the rock upon which ye are built, which is a sure foundation, a foundation whereon if men build they cannot fall.