The sum of the interior angles of a polygon is $4$ times the sum of its exterior angles. The polygon has:

The sum of the interior angles of a polygon is $4$ times the sum of its exterior angles. The polygon has:

$8$ sides
$10$ sides
$12$ sides
$14$ sides

Solution

$(n-2) \times 180 = 4 \times 360 = 1440 \Rightarrow n - 2 = 8 \Rightarrow n = 10$.

Asked in: IMO

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