(to be)/(for being) angry

Q1. What is his reason to be angry?
A1: He has no reason to be angry.
Q2. What is his reason for being angry?
A2: He has no reason for being angry.
Are these questions and answers OK?

Q1 sounds a little unnatural
A1 correct
Q2 correct
A2 correct

Thanks. Today you have answered my many questions.
Could you please make Q1 as natural using the phrase ‘to be angry’?

It’s not natural to use ‘to be’ at all. The question form would be ‘Why is he angry?’