The task shown on the right has aroused a lot of interest on Twitter. [For more such tasks, use the links above.]

The tag "World's hardest easy geometry problem" was coined by Keith Enevoldsen, who provides an interesting commentary on the task, and who traces its origins back to a journal published in the 1970s. Of course, it might have existed for much longer (perhaps since the big bang if you think god might have had a hand in it).

Enevoldsen says he worked on the task "for many hours over several days" before solving it. We had a similar experience, yet the task can be solved using only basic geometry in just a few steps - which you might hit upon in a matter of minutes!

Enevoldsen presents another such task on his website: *the world's second hardest easy geometry problem*. Are such tasks interesting? We're not sure - they don't seem to involve any kind of interesting (general) mathematical stucture, and Enevoldsen aptly describes them as **adventitious**.

However, **it is easy to get hooked**, sufficiently so in our case to see whether we could find **more such tasks**. We conducted a search using Geogebra which allowed us systematically to change the given angles in the task. To keep things manageable, we restricted ourselves to angles that were multiples of 5˚. In the event we came up with 8 more examples where the required angle AED turns out to be a nice round number, which one imagines therefore could be found using simple geometry. We have managed to do this with 6 of the tasks so far (some of which turned out to be *very* easy) but **we are still completely stuck on two of them**.

**The set of tasks can be found using the links at the top of the page**.

"10-10-20" refers to Enevoldsen's first task (where half the angle at C is 10˚, where the 'outer' angle at A is 10˚ and the 'outer' angle at B is 20˚). 10-20-30 is Enevoldsen's second task. The last task, 10-20-45, is a rogue - the size of angle E appears to be a round number, but in fact it isn't!

**Note**: In our versions of these tasks, the drawing **are** to scale and the value of the desired angle is **shown** - the challenge is to **prove** that this value is correct.

Using only elementary geometry, determine angle x.

*Provide a step-by-step proof.*