O valor de cada ângulo interno de um polígono é dada pela fórmula:
[tex]\Large\displaystyle\text{$\begin{gathered} \sf a_i = \frac{(n - 2) \cdot180 {}^{ \circ} }{n} \end{gathered}$}[/tex]
Onde:
[tex]\Large\displaystyle\text{$\begin{gathered} \begin{cases} \sf a_i = ângulo \,interno=? \\ \sf n = n\acute{u}mero \,de\, lados = 10\end{cases}\end{gathered}$}[/tex]
Calculando o valor do ângulo interno de um decágono pela fórmula temos que:
[tex]\Large\displaystyle\text{$\begin{gathered} \sf a_i = \dfrac{(n - 2) \cdot180 {}^{ \circ} }{n} \end{gathered}$}[/tex]
[tex]\Large\displaystyle\text{$\begin{gathered} \sf a_i = \frac{(10 - 2) \cdot180 {}^{ \circ} }{10} \end{gathered}$}[/tex]
[tex]\Large\displaystyle\text{$\begin{gathered} \sf a_i = \frac{8 \cdot180 {}^{ \circ} }{10} \end{gathered}$}[/tex]
[tex]\Large\displaystyle\text{$\begin{gathered} \sf a_i = \dfrac{1440 {}^{ \circ} }{10} \end{gathered}$}[/tex]
[tex]\Large\displaystyle\text{$\begin{gathered} \sf a_i = 144 {}^{ \circ} \end{gathered}$}[/tex]
Portanto, o valor de cada ângulo interno de um decágono é:
[tex]\Large\displaystyle\text{$\begin{gathered} \boxed{ \boxed{ \bf{144{}^{ \circ} }}}\end{gathered}$}[/tex]
