A person can use deadly force to protect themselves when they believe they are facing imminent threats of which of the following?

The correct answer is that a person can use deadly force to protect themselves when they believe they are facing imminent threats from aggravated robbery. This type of crime typically involves not just theft, but also the use of force or the threat of force, often involving weapons. The law recognizes aggravated robbery as a serious and violent offense that poses a significant threat to a person's life or well-being. When someone perceives they are in such a precarious situation, they may justifiably believe that they need to use deadly force to protect themselves.

In contrast, the other options relate to situations that typically do not involve an imminent threat of death or serious bodily injury. Minor theft is generally not viewed as a threat that justifies the use of deadly force. A physical confrontation could vary widely in severity, but unless it escalates to a life-threatening level, deadly force is not warranted. Vandalism usually involves property damage without a direct threat to a person's safety, which also does not justify the use of deadly force.