If the difference between the interior and exterior angles of a regular polygon is 144° then what is the number of sides of the polygon?
Given:
Difference between the interior and exterior angles of a regular polygon = 144º
Concept Used:
For a regular polygon with n sides:
Solution:
144 = [(n-2) × 180 / n] - (360 / n)
=> 144 = (180n - 360 - 360) / n
=> 144 = (180n - 720) / n
=> 144n = 180n - 720
=> 180n - 144n = 720
=> 36n = 720
=> n = 720 / 36
=> n = 20
Hence, the number of sides of the polygon is 20.
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