How to attach 10 AWG wire to LED strip lights?
Use a pigtail from the 10AWG wire to the strip light connector:



(this is just a representative image, not sure if these will fit your strip lights)

Just use wire-nuts to connect the 10AWG wires to the wires that go to the strip light connectors. Or solder and tape them.

If you have strip light connectors that aren't pre-wired, then create short jumpers with suitably sized wire to plug into the connector.