Question

a soma dos angulos internos com a dos angulos externos de um poligono regular vale 1800? gostaria de saber, por favor.

Answer 1

$S = ( n - 2) . 180 + 360 \\ \\ 1800 = (n-2) . 180 + 360 \\ \\ 1800 = 180n - 360 + 360 \\ \\ 180n = 1800 -\not 360 + \not 360 \\ \\ 180n = 1800\\ \\ \\ n = \dfrac{1800}{180} \\ \\ \\ n = 10$


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$d = \dfrac {n . (n - 3)}{2} \\ \\ \\ d = \dfrac {10 . (10 - 3)}{2} \\ \\ \\ d = \dfrac {10 . (7)}{2} \\ \\ \\ d = \dfrac {70}{2} \\ \\ \\ d = 35~diagonais$