Question

find the number of sides of a regula
polygon if each of it's interior
angle is [4pi/5)^c
​

Answer 1

Answer:

Step-by-step explanation:

Formula:

Interior angle of a regular polygon = ((n - 2)/n)*180 = ((n - 2)/n)*(pi)

Where n = number of sides of polygon

Given

Interior angle = (4*pi)/5

((n - 2)/n)*(pi) = (4*pi)/5

(n - 2)/n = 4/5

1 - (2/n) = 4/5

1 - (4/5) = 2/n

(5 - 4)/5 = 2/n

1/5 = 2/n

5 = n/2

n = 5*2 = 10

Number of sides = 10 ——> Answer

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