Geometry puzzle

I came across this geometry puzzle a while ago. Many people, even professional mathematicians seem to have problems with it, taking hours or days to solve it. Oddly enough, people with only basic knowledge of geometry seem to do a lot better, often a matter of minutes.


Given the following:

What is the angle ADE?

Note: it's not the answer that's important, as it can be measured easily. The thing is how to calculate the angle with the information given.


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