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The known angles are marked in degrees. We have to find the angle x.

I spent five minutes trying to do it on the board and then said I'd better take it away and get back to him.

I can solve the problem using trig. The answer is ##x## is 30 degrees - or at least so close to 30 degrees that my calculator rounds it to that when at maximum accuracy (it is reached by applying an arctan function to an expression involving trig functions of 20 and 30 degrees).

But I feel the problem should be solvable without trig, firstly because the answer is such a nice round number, equal to one of the angles in the triangle, and secondly because the problem was expected to be doable by a nine-year old (albeit a very smart one).

I've spent a bit of time trying to work out a construction that shows the answer to be 30 degrees using various line extensions, perpendiculars and so on, but I just keep hitting dead ends. Geometry was always one of my weaker subjects.

Does anybody out there think they can solve it without using trig?