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Read the following statements carefully and choose the correct option.
Statement I - Triangle is a polygon whose sum of exterior angles is double the sum of its interior angles.
Statement II - If the sum of interior angles of a polygon is double the sum of its exterior angles, then it is a hexagon.
Statement III - If the interior angles of a triangle are in the ratio $$1 \colon 2 \colon 3$$, then the ratio of its exterior angles is $$3 \colon 2 \colon 1$$.
For a triangle, exterior angles add up to $$360^\circ$$ and interior angles to $$180^\circ$$, so Statement I is true. If $$(n - 2) \times 180^\circ = 2 \times 360^\circ$$, then $$n = 6$$, so Statement II is true. Angles in the ratio $$1 \colon 2 \colon 3$$ are $$30^\circ, 60^\circ, 90^\circ$$, whose exterior angles $$150^\circ, 120^\circ, 90^\circ$$ are in the ratio $$5 \colon 4 \colon 3$$, so only Statement III is false.
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