how many diagonals does a 58 - sided convex polygon have?	Choose the correct answer
A) 870
B) 1125
C) 1595
D) 2560
E) 3190
<gadget id="calculator">factorial(58)</gadget>
<output>2_350_561_331_282_878_571_829_474_910_515_074_683_828_862_318_181_142_924_420_699_914_240_000_000_000_000</output>

<gadget id="calculator">58 - 2</gadget>
<output>56</output>

<gadget id="calculator">factorial(56)</gadget>
<output>710_998_587_804_863_451_854_045_647_463_724_949_736_497_978_881_168_458_687_447_040_000_000_000_000</output>

<gadget id="calculator">factorial(2)</gadget>
<output>2</output>

<gadget id="calculator">710_998_587_804_863_451_854_045_647_463_724_949_736_497_978_881_168_458_687_447_040_000_000_000_000 * 2</gadget>
<output>1_421_997_175_609_726_903_708_091_294_927_449_899_472_995_957_762_336_917_374_894_080_000_000_000_000</output>

<gadget id="calculator">2_350_561_331_282_878_571_829_474_910_515_074_683_828_862_318_181_142_924_420_699_914_240_000_000_000_000 / 1_421_997_175_609_726_903_708_091_294_927_449_899_472_995_957_762_336_917_374_894_080_000_000_000_000</gadget>
<output>1_653</output>

<result>C</result>
how many diagonals does a 58 - sided convex polygon have?
divide(factorial(58), multiply(factorial(subtract(58, const_2)), factorial(const_2)))
"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 ."