SOLUTION: How many sides does a polygon have if the sum of its interior angles is seven times the sum of its exterior angles?
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Question 1193137: How many sides does a polygon have if the sum of its interior angles is seven times the sum of its exterior angles? Found 2 solutions by Theo, greenestamps:Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website! the sum of the exterior angles of a polygon is always 360 degrees.
7 * 360 = 2520.
the sum of the interior angles of the polygon in question is 2520.
the sum of the interior angles of a polygon is equal to (n-2) * 180, therefore:
2520 = (n-2) * 180
solve for n-2 to get:
n-2 = 2520 / 180 = 14.
solve for n to get:
n = 16.
the polygon in question has 16 sides.
Since there is nothing in the statement of the problem that says anything about the polygon, the given information must be valid for any example of the polygon.
So we can assume the easy case where the polygon is regular.
Then the sum of each interior angle and the corresponding exterior angle is 180 degrees. And since the measure of the interior angle is 7 times the measure of the exterior angle, we have
x = exterior angle
7x = interior angle
The measure of the exterior angle of a regular polygon is 360, divided by the number of sides n:
