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Question 66014: Nellie flowers applied for the position of gardner for the estate of the retired eccentric mathematics professor Ben Dannett. Professor Dannett proposed the same problem to each gardening applicant. The first applicant who was clever enough to solve the problem would get gardening position-with a very handsome salary! Professor Dannett asked each applicant to draw the plans for a gardeb walk from the follow description, showing all deminsions: The outer edges of the walk form a regular polygon, with each side measuring 36 meters. The inner edges of the wall are parallel to the outer edges, and they form the same type of regular polygon, with each side measuring 30 meters. Each interior angle of a regular polygon measures 160 degrees. Needles to say, no applicant had solved the professor's conundrum before Nellie. Nellie solved the problem, and she got the job. How many sides do each of the two regular polygons have?
Answer by Cintchr(481)   (Show Source):
You can put this solution on YOUR website!The lengths of the sides doesn't matter. What matters here is the interior angle and how many sides there are. The formula for this is:
k = interior angle = 160
n = number of sides
Divide both sides by 180
reduce the left side
Cross multiply
Distribute
add 18 to both sides
subtract 8n from both sides
n = number of sides = 18
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