Apologies for the crude photo. If CD = DE then are angles ‘d’ and ‘e’ equal since they are opposite to sides CD and DE respectively?

Opposite side DE in the photo is angle c, not d. I think the answer to your question would be yes, but as it is now, your description and the info below the triangle aren’t stating the same thing

Ok so from the diagram I can see angle D is 90 and if it is then so what your stating is one side and hypotenuse are equal then the length of the other side will be 0 (Pythagoras theorem) if d is not 90 then angle(CDE)= angle(CED)