how many diagonals does a 59 - sided convex polygon have?  Choose the most appropriate option.
A) 1168	B) 1652	C) 2452	D) 3304	E) 4256
<gadget id="calculator">factorial(59)</gadget>
<output>138_683_118_545_689_835_737_939_019_720_389_406_345_902_876_772_687_432_540_821_294_940_160_000_000_000_000</output>

<gadget id="calculator">59 - 2</gadget>
<output>57</output>

<gadget id="calculator">factorial(57)</gadget>
<output>40_526_919_504_877_216_755_680_601_905_432_322_134_980_384_796_226_602_145_184_481_280_000_000_000_000</output>

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

<gadget id="calculator">40_526_919_504_877_216_755_680_601_905_432_322_134_980_384_796_226_602_145_184_481_280_000_000_000_000 * 2</gadget>
<output>81_053_839_009_754_433_511_361_203_810_864_644_269_960_769_592_453_204_290_368_962_560_000_000_000_000</output>

<gadget id="calculator">138_683_118_545_689_835_737_939_019_720_389_406_345_902_876_772_687_432_540_821_294_940_160_000_000_000_000 / 81_053_839_009_754_433_511_361_203_810_864_644_269_960_769_592_453_204_290_368_962_560_000_000_000_000</gadget>
<output>1_711</output>

<result>B</result>
how many diagonals does a 59 - sided convex polygon have?
divide(factorial(59), multiply(factorial(subtract(59, const_2)), factorial(const_2)))
a 59 - sided convex polygon has 59 vertices . if we examine a single vertex , we can see that we can connect it with 56 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 59 vertices can be connected with 56 vertices to create a diagonal then the total number of diagonals would be ( 59 ) ( 56 ) = 3304 however , we must recognize that we have counted every diagonal twice . to account for counting each diagonal twice , we must divide 3304 by 2 to get 1652 . the answer is b .