Depends on their personality and if they're conflict avoidant or conflict seeking.

(Unfortunately I've drafted my response for the scenario that someone is mad at you for something that you did or they think you did. If people are mad for other reasons but you're not the 'cause' of their anger, then some of this still applies. I'm adding this disclaimer because I don't want my comment to be accusatory and be read as though I assume that you have done anything wrong)

If they're conflict avoidant they may:

• give short answers to your questions where you'd expect something longer
• use words that suggest moderate agreement like 'okay', 'fine' rather than definite agreement or endorsement like 'sure' or 'great'
• leave the room when you enter, or shortly after
• avoid conversation

They are trying to get away from you, and will cut conversation short and distance themself from you. Being around you probably reminds them of what upset them, and they may need time to calm down and think through their response.

Their anger at you asking is likely to come because they expected you to have noticed from the above behaviour that they are mad. They may expect you to be the one to come forward and apologise.

In this case, what they may be expecting is either that you name specifically what you did to make them angry, if you can work it out or if it's applicable. Otherwise, if you don't, rather than asking "Are you angry" they may expect the apology first before they're willing to hear you out. Something like:

You: "Hey, I think I said/did something that upset you and I'm sorry if that was me. I'm not sure exactly was, but if you're okay with it, could you please help me understand what I did/said and how I can make amends"

Ideally, if they've had time to think, they may tell you what it is that upset them, and whether it was you, or someone else, or if they were mad and taking it out on you.

That's best case scenario. If they're resentful then even if you ask them what you did wrong they may like continue the same behaviour I listed in the dot points above.

In this case, they may need more space and time. You've extended the olive branch, so to speak, and the ball is in their court to accept the apology.

If they are resentful and want to get back at you, then, in addition to the behaviours above, they may do 'petty' things like:

• deliberately disrespect your personal space or property (enter your room, move your things, eat your food)
• unilaterally cancel shared commitments between you and them (pull out of dates without telling you, not do the dishes if it's their night, etc.)
• neglect care of things you care for (not water the plants, feed the dog)

Their motivation here is to deny you or harm things you enjoy while avoiding direct contact with you, and maintaining plausible deniability.

If the person is conflict seeking, unfortunately I don't have much experience with people like that.

Also this is mostly based on my experience with conflict with people in my life, so it's not an ironclad list of behaviours of upset people.