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      Question

      The ratio between the number of sides of two regular

      polygons is 1 : 2 and the ratio between their interior angle is 2 : 3. Then the number of sides of these polygons are respectively?
      A 4,8 Correct Answer Incorrect Answer
      B 5,10 Correct Answer Incorrect Answer
      C 3,6 Correct Answer Incorrect Answer
      D 6,12 Correct Answer Incorrect Answer

      Solution

      Let the side of polygon is = x, 2x So interior angle = ((N-2)×180)/N Where N = total number of sides, ((x-2)×180)/x : ((2x-2)×180)/2x = 2 : 3 (((x-2)×180)/x)/(((2x-2)×180)/2x) = 2/3 (2(x-2))/((2x-2)) = 2/3 3x - 6 = 2x - 2 x = 6 - 2 = 4 So, sides of polygon = 4, 8

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