Question

Os angulos externos de um poligono regular medem 20 graus . Determine o umero de diagonais desse poligono?

Answer 1

$\mathrm{A_e=\dfrac{360\°}{n}\ \to\ 20\°=\dfrac{360\°}{n}}\\\\ \mathrm{n=\dfrac{360\°}{20\°}\ \to\ n=18\ lados}\\\\ \mathrm{d=\dfrac{n(n-3)}{2}\ \to\ d=\dfrac{18(18 - 3)}{2}}\\\\ \mathrm{d=9.15}\ \to\ \mathbf{d=135\ diagonais}$