The hardest Euler problem

I have sorted the Euler problems from hardest to easiest,
and indeed the most interesting ones come up front.

This one gets me particularly stunned.

Find all quadrilaterals with angles (including those with diagonals).
that can be measured in whole degrees.
So a square fits the bill, because all those angles are 45 degrees.
They give an example of a non-trivial example with 20 and 50
degrees.

I cannot come up with something better than this
- guess all angles except one.
- calculate the last one using goniometric functions.
The problem states that if it is within 10-9 of a whole degree, it is
acceptable as a whole degree.
This is of course a nasty calculation.
Using fixed point calculations would even me more cumbersome.
I cannot find a way to do it exactly which would be more gratifying,
if only mathematically.

Takers anyone?

Groetjes Albert

--
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Albert van der Horst, UTRECHT,THE NETHERLANDS
Economic growth -- like all pyramid schemes -- ultimately falters.
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