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our sir told that the sum of the interior angles of an 'n' sided polygon is '(n-2)pie'.how?

our sir told that the sum of the interior angles of an 'n' sided polygon is '(n-2)pie'.how?

Grade:12

1 Answers

Anil Pannikar AskiitiansExpert-IITB
85 Points
10 years ago

Dear Vivek,

 

A quadrilateral has  4 sides, draw a diagonal and divide it into 2 traingles

so , Sum of angle  =  2 * 180 = 360

A pentagon has 5 sides, draw 2 diagonal and divide it into 3 traingles

so , Sum of angle  =  3 * 180 = 540

similarly. a hexagon has 6 sides, draw 3 diagonal and divide it into 4 traingles

so , Sum of angle  =  4* 180 = 720

 

so u can generalize, sum = ( n-2 )*180

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Askiitians Expert

Anil Pannikar

IIT Bombay

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