When dealing with others (loved ones, co-workers, customers, C Suite executives, absolutely anyone), it’s very useful, indeed vital, to see as they see. It doesn’t matter if you agree with them. It matters, however, that you strive to see matters as they see them. This is empathy. Don’t confuse empathy with sympathy (many people do); the two are different.
When dealing with someone who is exhibiting anger, see further, see deeper (by listening with all your senses) to what is hiding underneath and behind that anger. It is very often something which, when understood more deeply, grants you an opportunity to extend kindness, or some specific kind of support, to the person. His/her anger may be clever camouflage for something for which they need help. Diagnose a problem more clearly and let that drive your response.
And for those already thinking it, no, seeking to see what’s underneath/behind the anger so as to give you a more effective path of addressing it does not make you more susceptible to incurring a person’s aggression or violence. Depending on the totality of the situation, stop (physically or otherwise) a person from harming anyone. However, in order to most effectively extinguish the fire of anger (or to get to the root of any exhibited emotion), always seek what’s REALLY going on. Don’t be fooled by masks.