Question

10. The number of sides of two regular polygons are as 5:4 and the difference between the
angles is 9°. Find the number of sides of the polygons.
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Answer 1

Answer:

Let each side of one polygon be 5X

hence each side of other polygon be 4X

ATC

[{(n-2)180}÷n] - [{(n-2)180}÷n] = 9

[{(5X-2)180}÷5X] - [{(4X-2)180}÷4X] = 9

[{900X-360}÷5X] - [{720X-360}÷4X] = 9

(3600X-1440-3600X+1800)÷20X = 9

360÷20X = 9

360 = 9×20X

360 = 180X

X = 360÷180

X =2

each side of one polygon = 5X = 5×2 =10

each side of other polygon = 4X = 4×2

= 8