SOLUTION: The difference between the interior angles of two regular polygons is 40 degrees . the number of sides of one polygon is one-third of the other polygon. determine the number of sid

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Question 1117743: The difference between the interior angles of two regular polygons is 40 degrees . the number of sides of one polygon is one-third of the other polygon. determine the number of sides of each polygon. (4marks)
Answer by ikleyn(52887) About Me  (Show Source):
You can put this solution on YOUR website!
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Let n and m are the numbers of sides of the two polygons; n > m.



Then the exterior angles are  360%2Fn degs  and  360%2Fm degs respectively,

while the interior angles are  180-360%2Fn  and  180-360%2Fm degrees.



You have this system of two equations


180+-+360%2Fn - 180+-+360%2Fm = 40   (<<<---=== the difference)

n = 3m.



Simplify and solve 

360%2Fm - 360%2F%283m%29 = 40    (multiply both sides by 3m

360*3 - 360 = 40*3m


720 = 120m  ====>  m = 720%2F120 = 6.



Answer.  The numbers of sides are  6  and  18.