Question

ayudaaa el curso es geometria pls ayuda doy coronita ​

Answer 1

Explicación paso a paso:

Para el Polígono de n = 3

=> Si = 180(n - 2) => 180(3 - 2) => 180(1) = 180°

=> m∠i = 180(n - 2)/n => 180(3- 2)/3 => 180(1)/3 => 60°

=> Se = 360°

=> m∠e = 360/n => 360/3 => 120°

=> N° de Diagonales = n(n - 3)/2 => 3(3 - 3)/2 => 3(0)/2 => 0 diagonales

Para el Polígono de n = 4

=> Si = 180(n - 2) => 180(4 - 2) => 180(2) => 360°

=> m∠i = 180(n - 2)/n => 180(4 - 2)/4 => 180(2)/4 => 360/4 => 90°

=> Se = 360°

=> m∠e = 360/n => 360/4 => 90°

=> N° de Diagonales = n(n - 3)/2 => 4(4 - 3)/2 => 4(1)/2 => 2 diagonales

Para el Polígono de n = 5

=> Si = 180(n - 2) => 180(5 - 2) => 180(3) = 540°

=> m∠i = 180(n - 2)/n => 180(5 - 2)/5 => 180(3)/5 => 540/5 => 108°

=> Se = 360°

=> m∠e = 360/n => 360/5 => 72°

=> N° de Diagonales => n(n - 3)/2 => 5(5 - 3)/2 => 5(2)/2 => 5 diagonales

Para el Polígono de n = 6

=> Si = 180(n - 2) => 180(6 - 2) => 180(4) = 720°

=> m∠i = 180(n - 2)/n => 180(6 - 2)/6 => 180(4)/6 => 720/6 => 120°

=> Se = 360°

=> m∠e = 360/n => 360/6 => 60°

=> N° de Diagonales = n(n - 3)/2 => 6(6 - 3)/2 => 6(3)/2 => 18/2 => 9 diagonales

Para el Polígono de n = 7

=> Si = 180(n - 2) => 180(7 - 2) => 180(5) = 900°

=> m∠i = 180(n - 2)/n => 180(7 - 2)/7 => 180(5)/7 => 900/7 => 128, 57°

=> Se = 360°

=> m∠e = 360/n => 360/7 => 51,43°

=> N° de Diagonales = n(n - 3)/2 => 7(7 - 3)/2 => 7(4)/2 => 28/2 => 14 diagonales

Para el Polígono de n = 8

=> Si = 180(n - 2) => 180(8 - 2) => 180(6) => 1080°

=> m∠i = 180(n - 2)/n => 180(8 - 2)/8 => 180(6)/8 => 1080/8 => 135°

=> Se = 360°

=> m∠e = 360/n => 360/8 => 45°

=> N° de Diagonales = n(n - 3)/2 => 8(8 - 3)/2 => 8(5)/2 => 40/2 => 20 diagonales

Para el Polígono de n = 9

=> Si = 180(n - 2) => 180(9 - 2) => 180(7) = 1260°

=> m∠i = 180(n - 2)/n => 180(9 - 2)/9 => 180(7)/9 => 1260/9 => 140°

=> Se = 360°

=> m∠e = 360/n => 360/9 => 40°

=> N° de Diagonales = n(n - 3)/2 => 9(9 - 3)/2 => 9(6)/2 => 54/2 => 27 diagonales

Para el Polígono de n = 10

=> Si = 180(n - 2) => 180(10 - 2) => 180(8) = 1440°

=> m∠i = 180(n - 2)/n => 180(10 - 2)/10 => 180(8)/10 =>1440/10 => 144°

=> Se = 360°

=> m∠e = 360/n => 360/10 => 36°

=> N° de Diagonales = n(n - 3)/2 => 10(10 - 3)/2 => 10(7)/2 => 70/2 => 35 diagonales

Para el Polígono de n = 12

=> Si = 180(n - 2) => 180(12 - 2) => 180(10) => 1800°

=> m∠i = 180(n - 2)/n => 180(12 - 2)/12 => 180(10)/12 => 1800/12 => 150°

=> Se = 360°

=> m∠e = 360/n => 360/12 => 30°

=> N° de Diagonales = n(n - 3)/2 => 12(12 - 3)/2 => 12(9)/2 => 108/2 => 54 diagonales

Para el Polígono de n = 20

=> Si = 180(n - 2) => 180(20 - 2) => 180(18) = 3240°

=> m∠i = 180(n - 2)/n => 180(20 - 2)/20 => 180(18)/20 => 3240/20 => 162°

=> Se = 360°

=> m∠e = 360/n => 360/20 => 18°

=> N° de Diagonales = n(n - 3)/2 => 20(20 - 3)/2 => 20(17)/2 => 340/2 => 170 diagonales

Para el Polígono de n = 30

=> Si = 180(n - 2) => 180(30 - 2) => 180(28) => 5040°

=> m∠i = 180(n - 2)/n => 1180(30 - 2)/30 => 180(28)/30 = 5040/30 => 168°

=> Se = 360°

=> m∠e = 360/n => 360/30 => 12°

=> N° de Diagonales = n(n - 3)/2 => 30(30 - 3)/2 => 30(27)/2 => 810/2 => 405 diagonales

Para el Polígono de n = 36

=> Si = 180(n - 2) => 180(36 - 2) => 180(34) = 6120°

=> m∠i = 180(n - 2)/n =>  180(36 - 2)/36 => 180(34)/36 = 6120/36 => 170°

=> Se = 360°

=> m∠e = 360/n => 360/36 => 10°

=> N° de Diagonales = n(n - 3)/2 => 36(36 - 3)/2 => 36(33)/2 => 1188/2 => 594 diagonales

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