Handing me the $10,000 lottery ticket, his face broke into a broad smile.
(Rewrite the following sentence so that the verbal doesn't dangle)
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He handed me the $10,000 lottery ticket, and his face broke into a broad smile.
To rewrite the sentence so that the verbal doesn't dangle, we simply add a subject that can perform the action of handing the ticket. In this case, "he" is the subject who performs the action of handing the ticket, and the sentence now makes clear that it was he who handed over the ticket before his face broke into a broad smile.