If the sum of the measures of the interior angles of a convex n-gon is equal to the sum of the measures of the exterior angles, how many sides does the n-gon have?   I have no clue as to how to...

If the sum of the measures of the interior angles of a convex n-gon is equal to the sum of the measures of the exterior angles, how many sides does the n-gon have?

 

I have no clue as to how to answer this question! please help!

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pramodpandey | College Teacher | (Level 3) Valedictorian

Posted on

Sum all interior angles of n gone=(n-2)x180     (i)

Sum of all exterior angles of n gone= 360        (ii)

from given condition

`(n-2)xx180=360`

`n-2=360/180`

`n-2=2`

`n=4`

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