Question

O angulo externo de um poligono regular mede 20. Determine o numero de diagonais desse poligono?

Answer 1

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