SOLUTION: The sum of the interior angles of a polygon is twice the sum of its exterior angles. How many sides does the polygon have ?

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Question 1122221: The sum of the interior angles of a polygon is twice the sum of its exterior angles. How many sides does the polygon have ?
Found 2 solutions by Theo, ikleyn:
Answer by Theo(13342) About Me  (Show Source):
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the polygon has 6 sides.

the sum of the exterior angles of a polygon is always 360 degrees.

the sum of the interior angles of a polygon is equal to 180 * (n - 2).

n is equal to the number of sides of the polygon.

if the sum of the interior angles is twice the sum of the exterior angles, then the sum of the interior angles has to be 720 degrees.

720 = 180 * (n - 2)
divide both sides of this equation by 180 to get 720/180 = n - 2
simplify to get 4 = n - 2
solve for n to get n = 6


Answer by ikleyn(52775) About Me  (Show Source):
You can put this solution on YOUR website!
.
It is possible if and only if each interior angle is twice its exterior angle.


Since these angles are supplementary, it is possible only if all interior angles are 120 degrees each.


Hence, the polygon has 6 sides (hexagon).