Question

Em um pligono regular a medida de cada ângulo externo e 24°.esse polígono tem quantoas diagonais

Answer 1

$\large\boxed{\begin{array}{l}\rm n=\dfrac{S_e}{a_e}\\\\\rm n=\dfrac{360\diagup\!\!\!^\circ}{24\diagup\!\!\!^\circ}\\\\\rm n=15\\\rm d=\dfrac{n\cdot(n-3)}{2}\\\\\rm d=\dfrac{15\cdot(15-3)}{2}\\\\\rm d=\dfrac{15\cdot \diagdown\!\!\!\!\!\!12^6}{\diagdown\!\!\!\!2}\\\\\rm d=15\cdot6\\\rm d=90\end{array}}$