the number of sides of a regular polygon if each of its interior angle=(4π/5)^c is
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Answer:no. of sides =10
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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
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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