Question 205368
There are two polygons. The larger one has three times as many sides as the smaller one, and its angle sum is four times bigger. How many sides has the smaller polygon?
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If a polygon has x sides, then each angle of this polygon is:
180 - (360/x)
the angle sum of this polygon 
= x * (180 - (360/x))
= 180x - 360 

let:
number of smaller polygon's side = a
angle sum of smaller polygon = 180a - 360
number of larger polygon's side = b
angle sum of larger polygon = 180b - 360 

b = 3a
180b - 360 = 5 * (180a - 360)
4 times bigger is 5 times as big.
4 times bigger is 5 times as big.
4 times bigger is 5 times as big.
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How much is 1 times bigger, or 100% bigger? It's 2 times as big.
180*(3a) - 360 = 900a - 1800
540a - 360 = 900a - 1800
a = 4