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

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.
Answer by htmentor(1343) (Show Source): You can put this solution on YOUR website!
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.
===========================================================
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.
RELATED QUESTIONS
Gary makes custom metal signs. He has a sheet of metal that is 6 feet by 12 and want to... (answered by fractalier)

It's been many years since I've been in school. If I have an 8 foot long piece of metal... (answered by edjones)

Willy Wanka's factory Has a machine that can make 1000 chocolates bars in5 hours. A new... (answered by ikleyn)

I need help with notations. I don't understand which signs mean what. I have a question... (answered by stanbon)

A factory makes use of two basic machines, A and B, which turn out two different... (answered by ikleyn)

At a metal melting factory, a machinist melts two barrels of metal and mixes them... (answered by josmiceli)

A rectangular piece of sheet metal has a length that is 2 times its width. In each... (answered by josgarithmetic)

An employee looks out his office window at a factory across the street. He estimates his... (answered by josmiceli)

A rectangular piece of sheet metal has a length that is 4.3 times its width. In each... (answered by Boreal)