Learn Arabic (Modern Standard): هم ليسوا غاضبين.

In Arabic, ليس acts like a verb and must match the subject in gender and number. Since the subject is "they" (masculine plural), we conjugate it by adding the plural ending ـوا, making it ليسوا.

I learned that the masculine plural of "angry" is غاضبون. Why is it spelled غاضبين here?

This is a key rule for using ليس. It changes the state (case) of the word that describes the subject into the accusative case (called Mansub). For regular masculine plural words, this means the ـون (-oon) ending changes to ـين (-een). Therefore, غاضبون becomes غاضبين after ليسوا.

Could we drop the هم at the beginning and just say ليسوا غاضبين?

Yes, absolutely! Because ليسوا already has the "they" ending built into it, the sentence ليسوا غاضبين is perfectly correct and means the exact same thing. Including هم just makes it a standard nominal sentence and adds a little bit of emphasis on "they".

Why is there an extra Alif (ا) at the very end of ليسوا?

That Alif is totally silent. In Arabic spelling, whenever a verb ends with the plural Waw (و), we add a silent Alif at the end. It acts as a visual marker to show that the Waw means "they" and isn't just a regular letter in the root of the word.