SOLUTION: 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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Question 205368This question is from textbook Longman Mathematics for IGCSE Book 1
: 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? This question is from textbook Longman Mathematics for IGCSE Book 1

Found 2 solutions by alicealc, Alan3354:
Answer by alicealc(293) (Show Source):
You can put this solution on YOUR website!
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 = 4 * (180a - 360)
180*(3a) - 360 = 720a - 1440
540a - 360 = 720a - 1440
1440 - 360 = 720a - 540a
1080 = 180a
a = 1080/180 = 6

so, the smaller polygon has 6 sides

Answer by Alan3354(69443) (Show Source):
You can put this solution on YOUR website!
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?
-------------------
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