Question 2

The number of equiangular octagons fixing 6 consecutive sides is

Solution

Every angle of an equiangular octagon is $$135^\circ$$, so the direction of each side is fixed, turning by $$45^\circ$$ each time. Once six consecutive sides are fixed, the octagon must close, which gives two linear equations for the two remaining side lengths along two non-parallel directions. These have exactly one solution, so the octagon is uniquely determined (when both lengths come out positive). The number is therefore at most one, which matches none of a, b or d, so the answer is "None of these".

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