Question

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

Answer 1

Decágono = 10 lados

ai = Si/n
Si = 180 . (n - 2)
Si = 180 . (10-2)
Si = 180 . 8
Si = 1440

ai = 1440/10
ai = 144°
O angulo interno mede 144°.

ai + ae = 180
144 + ae = 180
ae = 180 - 144
ae = 36°
O ângulo externo mede 36°.
Espero ter ajudado e bons estudos!

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:

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

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

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