How many diagonals in a 50-gon? - Answers

for any polygon with 'n' number of sides, the number of diagonals will be n(n-3) / 2 if n is 50, no. of diagonals will be 50(50-3)/2 = 47*25 = 1175 how do you get it? take any polygon, say septagon i.e. with 7 sides if you take 1 vertice, remainig vertices will be 7-1 that is 6. there will be 2 consecutive vertices for any vertice, so here, this one has 2 consecutive vertices(its always like that) so the remaining vertices is 6-2 that is 4. remember : a diagonal connects non consecutive vertices so you know that from one vertice, there will be 4 diagonals. multiply it by the total no. of vertices(here 7) 4*7 = 28 now divide this by 2 (since 2 vertices share the same diagonal) therefore, 28/2 = 14 which is the no. of diagonals in a septagon. so for an n-gon, the number of diagonals will be n(n-3) / 2 hope it helps! p.s. i figured it out myself during math class. then i tried it on many polygons.