SOLUTION: The ratio of each interior angles to each exterior angle of a regular polygon is 4:1. Find the number of sides of the polygon

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 Click here to see ALL problems on Polygons Question 624495: The ratio of each interior angles to each exterior angle of a regular polygon is 4:1. Find the number of sides of the polygonAnswer by Theo(3458)   (Show Source): You can put this solution on YOUR website!I = interior angle E = exterior angle the sum of I and E is equal to 180 (they are supplementary). the ratio of I to E is 4:1 this means that I = 4E since I + E = 180 and I = 4E, you get: 4E + E = 180 which simplifies to: 5E = 180 which results in: E = 36 degrees since the sum of the exterior angles of a polygon is equal to 360 degrees, you divide 360 by 36 to get the number of sides of the polygon. 360/36 = 10 which means the polygon has 10 sides which makes it a decagon. working back from the knowledge that the polygon is a decagon, we can use the formula for the interior angle of a polygon to find the interior angle which should be equal to 180 - 36 = 144 degrees. the formula for the interior angles of a polygon is: I = 180(n-2)/n since the decagon has 10 sides, this formula becomes: I = 180(8)/10 which is equal to 1440/10 which is equal to 144 degrees. Since I = 144, E = 180 - 144 = 36 degrees. Decagon is confirmed. One last confirmation: ratio of I to E is 4:1 144:36 is the same as 4:1 because 4*36 = 144. We're good all around.