Question

si la relacion entre angulo interuor y exterior de un poligono regular es de 7 a 2 cuAntas diagonales tiene?

Answer 1

$Hola \\ \\\acute{A}ngulos\begin{cases} \angle_i= \frac{180\°(n-2)}{n} \\ \\ \angle_e=360\° \end{cases} \\ \\ Indica~que: \\ \\ \frac{ \frac{180\°(n-2)}{n} }{360\°} = \frac{7}{2} ~~---\ \textgreater \ resolviendo~nos~queda: \\ \\ n-2=7 \\ \\ \boxed{n=9} \\ \\ \mathbb{ttttttttttttttttttttttttttttttttttt} \\ Respondiendo~la~pregunta: \\ \#D= \frac{n(n-3)}{2} ~~--\ \textgreater \ donde~[n=9], reemplazando \\ \\ \#D= \frac{9(9-3)}{2} \\ \\\boxed{\boxed{ \#D=27}}$


$\mathbb{qqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqq}\\~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~Espero~te~sirva, saludos!!$