Star Study - n pointed total

Because each internal angle of n-pointed star is equal to haft of in-center angle with the same arc. If n is odd, these in-center angles are separated and cover whole circle, so sum of them is: $360^{0}$ Hence sum of internal angles of n-pointed star is: $180^{0}$ If n is even, these in-center angles pairwise overlap each other in haft of each. So sum of these angles is: $360 \times 2 = 720 ^{0}$ So sum of internal angles of n-pointed star is: $360^{0}$ Answer is: $\boxed{180^{0}: n=2k+1, 360^{0}: n=2k}$

Use some mind ! When there were 5 sides .... Sum was 180 When there were 10 sides ..... sum was 360 That means If it will be an odd side than 180 and if it will be an even side than 360 !! Nice Na ....... :) :)

since 5 star angles( odd numbers)have sum total of 180 degrees and 10 star angles have 360( even numbers),therefore in a circle ,with odd no of vertices it will be 180 degree and with even nos of vertex this will be 360 degrees. K.K.GARG,India