Deer are herbivores. Since we know this, we know that deer don't eat meat.
Since deer don't eat meat from other animals or insects, they only eat plant life.
Plants get their energy from the sun through photosynthesis, which makes sugar so the plant can have energy.
The deer then eats the plant which has sugar stored in it and uses that energy to live and function.
-The deer cannot do photosynthesis, so it can't get energy from the sun.
-The deer can't eat meat, so it can't get energy from that either
-The only way for the deer to get energy is by eating the plants
But in the real world, there are a few plants that get energy by eating things, but deer don't eat those plants. Or at least not that I know of.
I hope I helped :)