SOLUTION: A factory makes metal signs. Its machines have been set at an angle that allows them to cut out pentagonal direction signs. How much should this angle be increased or decreased to

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Question 475690: A factory makes metal signs. Its machines have been set at an angle that allows them to cut out pentagonal direction signs. How much should this angle be increased or decreased to change the machines so they will cut out metal shapes used to make standard octagonal (8 sides) stop signs? Assume all signs to be regular polygons.
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A factory makes metal signs. Its machines have been set at an angle that allows them to cut out pentagonal direction signs. How much should this angle be increased or decreased to change the machines so they will cut out metal shapes used to make standard octagonal (8 sides) stop signs? Assume all signs to be regular polygons.
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For a regular polygon with n sides, each angle measures
(n-2)180/n
A pentagon has 5 sides, so each angle is
(5-2)180/5 = 108 deg.
An octagon has 8 sides, so each angle is
(8-2)180/8 = 135 deg.
So the angle needs to be increased by 27 deg.