I serach for my question But I didn't find same question. my question is:
if we have Inscribed quadrilateral, then we can easily prove that $\alpha = \beta $
But If we know that $\alpha = \beta $, then how can we prove that our quadrilateral is Inscribed in a circle?
I do something for this but I am not sure about it. can you verify it?
we know that $\alpha = \beta $ but we suppose that our quadrilateral ABCD is not Inscribed. Then we make ABCF that is Inscribed quadrilateral so because $\alpha = \beta $ we have $\smallfrown EC = \smallfrown CF$ (I don't know how to make it) and It's not true so our quadrilateral ABCD is Inscribed.