Question

qual a medida do ângulo interno e a do ângulo externo de em decágono regular ?

Answer 1

formula para o angulo interno
(n-2)180/n
(10-2)180/10
8*180/10
1440/10
144


o angulo externo juntando com o angulo interno é igual a 180°
144°+ x = 180
x = 180-144
x = 36 °
angulo interno igual a 144°
externo 36°

Answer 2

$\Large\displaystyle\begin{gathered} \sf a_i = 144 {}^{ \circ}\end{gathered}$

$\Large\displaystyle\begin{gathered} \sf a_e = 36 {}^{ \circ} \end{gathered}$

Explicação passo-a-passo:

Ângulo interno:

$\Large\displaystyle\text{ \begin{gathered} \sf a_i = \dfrac{(n - 2) \cdot180 {}^{ \circ} }{n} \end{gathered} }$

$\Large\displaystyle\text{ \begin{gathered} \sf a_i = \frac{(10 - 2) \cdot180 {}^{ \circ} }{10} \end{gathered} }$

$\Large\displaystyle\text{ \begin{gathered} \sf a_i = \frac{8 \cdot180 {}^{ \circ} }{10} \end{gathered} }$

$\Large\displaystyle\text{ \begin{gathered} \sf a_i = \dfrac{1440 {}^{ \circ} }{10} \end{gathered} }$

$\Large\displaystyle\begin{gathered} \sf a_i = 144 {}^{ \circ} \end{gathered}$

Ângulo externo:

$\Large\displaystyle\text{ \begin{gathered} \sf a_e = \frac{360 {}^{ \circ} }{n} \end{gathered} }$

$\Large\displaystyle\text{ \begin{gathered} \sf a_e = \frac{360 {}^{ \circ} }{10} \end{gathered} }$

$\Large\displaystyle\begin{gathered} \sf a_e = 36 {}^{ \circ} \end{gathered}$