SOLUTION: The interior angle of a regular polygon is more by 144degree than its exterior angle.find the number of sides of regular polygon.

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Question 1132141: The interior angle of a regular polygon is more by 144degree than its exterior angle.find the number of sides of regular polygon.
Answer by ikleyn(52781) About Me  (Show Source):
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The interior angle of a regular polygon is more by 144 degree than its exterior angle. Find the number of sides of regular polygon.
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You are given


Int + Ext = 180      (1)

Int - Ext = 144      (2)     ("The interior angle of a regular polygon is more by 144degree than its exterior angle.")


Subtract equations (2) from equation (1) to get


    2*Ext = 180 - 144 = 36  degrees  ====>  Ext = 36%2F2 = 18 degrees.


Now use the fact that the sum of all exterior angles of a polygon is  equal to 360 degrees:


    n*Ext = 360,    which implies   n = 360%2F18 = 20.


ANSWER.  The number of sides of the given regular polygon is 20.

Solved.