Question

Please explain your answer
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Answer 1

Step-by-step explanation:

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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 = aangle sum of smaller polygon = 180a - 360number of larger polygon's side = bangle sum of larger polygon = 180b - 360 b = 3a180b - 360 = 4 * (180a - 360)180*(3a) - 360 = 720a - 1440540a - 360 = 720a - 14401440 - 360 = 720a - 540a1080 = 180aa = 1080/180 = 6 so, the smaller polygon has 6 sides

Answer 2

Answer:

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