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The smallest positive integer $$n$$ for which it is possible to draw an $$n$$-gon whose vertex angles all measure either $$163^\circ$$ or $$171^\circ$$ is
Correct Answer: 24
Suppose $$k$$ angles are $$163^\circ$$ and the other $$n-k$$ angles are $$171^\circ$$. Equating their sum to $$(n-2)180^\circ$$ gives $$9n+8k=360$$. This forces $$n$$ to be a multiple of $$8$$, and the first feasible choice is $$n=24$$ with $$k=18$$.
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