Typically the person you hit would file a claim with your insurance company for the damages his car received from your truck. If the other party for some reason would rather go through his insurance company you could indeed pay his deductible. Even if you do pay his deductible his insurance company might still decide to subrogate with your insurance company to get reimbursed for the monies they spent on the claim. State laws might vary so check with your insurance company to see how they suggest you deal with the claim.
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