Question

Determune a medida de CADA ângulo interno e CADA ângulo externo dos polígonos. Em seguuda determine o nunero de diagonais.

A) Eneagono ( 9 lados):


B ) Dodecágono ( 12 lados):

Answer 1

Eneágono- 27 diagonais
Dodecágono- 54 diagonais

Answer 2

a) Eneágono (9 lados):
$a _{i}= \frac{180^{o}(n-2) }{n} \\ a_{i} = \frac{180^{o}(9-2) }{9} \\ a_{i} = 20^{o}(7) \\ a_{i}=140^{o} \\ \\ a_{e}= \frac{360^{o} }{n} \\ a_{e} = \frac{360^{o} }{9} \\ a_{e} =40^{o} \\ \\ d= \frac{n(n-3)}{2} \\ d= \frac{9(9-3)}{2} \\ d= \frac{9(6)}{2} \\ d= \frac{54}{2} \\ d= 27$
b) Dodecágono (12 lados):
$a _{i}= \frac{180^{o}(n-2) }{n} \\ a_{i} = \frac{180^{o}(12-2) }{12} \\ a_{i} = 15^{o}(10) \\ a_{i}=150^{o} \\ \\ a_{e}= \frac{360^{o} }{n} \\ a_{e} = \frac{360^{o} }{12} \\ a_{e} =30^{o} \\ \\ d= \frac{n(n-3)}{2} \\ d= \frac{12(12-3)}{2} \\ d= \frac{12(9)}{2} \\ d= \frac{108}{2} \\ d= 54$