75. An "n-point star" is formed as follows : the sides of a convex polygon are numbered consecutivity \( 1,2,3, \ldots \ldots k , \ldots \ldots n , n \geq 5 \); for all \( n \) values of \( k \); sides \( k \) and \( k +2 \) are non parallel, sides \( n +1 \) and \( n +2 \) being respectively identical with sides 1 and 2 ; prolong the \( n \) pairs of sides numbered \( k \) and \( k +2 \) unit they meet. Find the sum of the interior angles at the \( n \) points of the star.

Question

75. An "n-point star" is formed as follows : the sides of a convex polygon are numbered consecutivity \( 1,2,3, \ldots \ldots k , \ldots \ldots n , n \geq 5 \); for all \( n \) values of \( k \); sides \( k \) and \( k +2 \) are non parallel, sides \( n +1 \) and \( n +2 \) being respectively identical with sides 1 and 2 ; prolong the \( n \) pairs of sides numbered \( k \) and \( k +2 \) unit they meet. Find the sum of the interior angles at the \( n \) points of the star.