In the below sketch, we have angle $\beta$ given, and a right angle $\angle CEB$ and a right angle $\angle CED$. The problem asked to show that $\triangle CEB$ is congruent to $\triangle CED$.

[![enter image description here](https://i.stack.imgur.com/rkyuu.jpg)](https://i.stack.imgur.com/rkyuu.jpg)

They use ASA for that, by saying that because $\beta$ is equal to $\angle DCE$ without further justification, but is that so obvious from the given information? It's obvious of course why ASA works after we can find $\angle DCE = \beta$, but it's not so clear to me how to justify this claim.