Icosagon part-2

Geometry Level 3

What is the sum of interior angles of a polygon with 35 diagonals?


The answer is 1440.

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Akhil Bansal by Akhil Bansal , 22, India

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3 solutions

Akhil Bansal
Jul 21, 2015

No. of polygon diagonals=35.
No. of diagonals of polygon having n sides= n ( n − 3 ) 2 \frac{n(n-3)}{2} .
Hence, no. of sides of polygon is 10.
and as mentioned in part-1, sum of interior angle of polgon of n sides is 180(n-2)= 180(8)= 1440


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It is n × ( n − 3 ) 2 \dfrac{n\times (n-3)} {2} and not what you have written. Kindly correct it.

Krishna Ar - 5 years, 10 months ago

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Thnx krishna

Akhil Bansal - 5 years, 10 months ago

He also wrote correct

Hadia Qadir - 5 years, 10 months ago

what's the difference between [n(n-3)]/2 and [n x (n-3)]/2 .........

Mayank Pershad - 5 years, 10 months ago
Hadia Qadir
Jul 26, 2015

the polygon is a decagon and the sum of the interior angles is 1440

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Luis Lopez
Jul 24, 2015

35=n(n-3)/2 => n^2-3n-70=0 => n=10 La suma de los ángulos internos de un polígono es (n-2) 180 y en el decágono n=10 por lo tanto la suma es 8 180= 1440.

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