Правилни многоуглови – први део

Текст задатака објашњених у видео предавању.

Пр.1) Израчунати унутрашњи и спољашни угао правилног:

(а) осмоугла      (б) петнаестоугла.

Пр.2) Израчунати централни угао правилног:

(а) деветоугла      (б) дванаестоугла.

Пр.1) 

\[\begin{array}{*{20}{c}}
\begin{gathered}
\underline {n = 11} \hfill \\
\alpha ,{\alpha _1} = ? \hfill \\
\begin{array}{*{20}{c}}
\begin{gathered}
{\alpha _1} = \frac{{{{360}^ \circ }}}{n} \hfill \\
{\alpha _1} = \frac{{{{360}^ \circ }}}{8} \hfill \\
{\alpha _1} = {45^ \circ } \hfill \\
\end{gathered} &\begin{gathered}
\alpha + {\alpha _1} = {180^ \circ } \hfill \\
\alpha = {180^ \circ } - {\alpha _1} \hfill \\
\alpha = {180^ \circ } - {45^ \circ } \hfill \\
\alpha = {135^ \circ } \hfill \\
\end{gathered}
\end{array} \hfill \\
\end{gathered} &\begin{gathered}
\underline {n = 15} \hfill \\
\alpha ,{\alpha _1} = ? \hfill \\
\begin{array}{*{20}{c}}
\begin{gathered}
{\alpha _1} = \frac{{{{360}^ \circ }}}{n} \hfill \\
{\alpha _1} = \frac{{{{360}^ \circ }}}{{15}} \hfill \\
{\alpha _1} = {24^ \circ } \hfill \\
\end{gathered} &\begin{gathered}
\alpha + {\alpha _1} = {180^ \circ } \hfill \\
\alpha = {180^ \circ } - {\alpha _1} \hfill \\
\alpha = {180^ \circ } - {24^ \circ } \hfill \\
\alpha = {156^ \circ } \hfill \\
\end{gathered}
\end{array} \hfill \\
\end{gathered}
\end{array}\]

Пр.2) 

\[\begin{array}{*{20}{c}}
\begin{gathered}
\underline {n = 11} \hfill \\
\varphi = ? \hfill \\
\varphi = \frac{{{{360}^ \circ }}}{n} \hfill \\
\varphi = \frac{{{{360}^ \circ }}}{9} \hfill \\
\varphi = {40^ \circ } \hfill \\
\end{gathered} &{}&\begin{gathered}
\underline {n = 12} \hfill \\
\varphi = ? \hfill \\
\varphi = \frac{{{{360}^ \circ }}}{n} \hfill \\
\varphi = \frac{{{{360}^ \circ }}}{{12}} \hfill \\
\varphi = {30^ \circ } \hfill \\
\end{gathered}
\end{array}\]