"Do you know why they are angry?"
吗 indicates that this is a yes/no question, so it's extremely important. Note the difference between the first and second sentences:
你喜欢去公园。--> You like to go to the park.
你喜欢去公园吗？ --> Do you like to go to the park?
你喜不喜欢去公园? --> Do you like to go to the park?
Likewise, the meaning of this sentence changes dramatically without 吗.
你知道他们为什么生气吗？--> Do you know why they're angry?
你知道他们为什么生气。--> You know why they're angry.
The Collins Dictionary reference for 吗 can be found here: https://www.collinsdictionary.com/dictionary/chinese-english/%E5%90%97