How many diagonals does a 58-sided convex polygon have?
Options:
A) 870
B) 1125
C) 1595
D) 2560
E) 3190

Rationale: "a 58 - sided convex polygon has 58 vertices . if we examine a single vertex , we can see that we can connect it with 55 other vertices to create a diagonal . note that we ca n ' t connect the vertex to itself and we ca n ' t connect it to its adjacent vertices , since this would not create a diagonal . if each of the 58 vertices can be connected with 55 vertices to create a diagonal then the total number of diagonals would be ( 58 ) ( 55 ) = 3190 however , we must recognize that we have counted every diagonal twice . to account for counting each diagonal twice , we must divide 3190 by 2 to get 1595 . the answer is c ."
Answer: C