Паралелограм

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Пр.1)   Израчунати све унутрашње и спољашње углове паралелограма

            ако је:

            а) један унутрашњи угао ${54^ \circ }$

\[\begin{array}{*{20}{c}}
\begin{gathered}
\alpha = {54^ \circ } \hfill \\
\alpha = \gamma = {54^ \circ } \hfill \\
\alpha + \beta = {180^ \circ } \hfill \\
{54^ \circ } + \beta = {180^ \circ } \hfill \\
\beta = {180^ \circ } - {54^ \circ } \hfill \\
\beta = {126^ \circ } \hfill \\
\beta = \delta = {126^ \circ } \hfill \\
\end{gathered} &\begin{gathered}
{\alpha _1} = {180^\circ } - \alpha \hfill \\
{\alpha _1} = {180^\circ } - {54^ \circ } \hfill \\
{\alpha _1} = {126^ \circ } \hfill \\
{\alpha _1} = {\gamma _1} = {126^ \circ } \hfill \\
{\beta _1} = {180^ \circ } - \beta \hfill \\
{\beta _1} = {180^ \circ } - {126^ \circ } \hfill \\
{\beta _1} = {54^ \circ } \hfill \\
\end{gathered} &\begin{gathered}
{\delta _1} = {\beta _1} \hfill \\
{\delta _1} = {54^ \circ } \hfill \\
\hfill \\
\hfill \\
\hfill \\
\hfill \\
\hfill \\
\end{gathered}
\end{array}\]

            б) збир два унутрашња угла ${157^ \circ }$

$\alpha + \gamma = {157^ \circ } $

$\alpha = \gamma $
$2\gamma = {157^ \circ } $
$\gamma = {157^ \circ }:2 $
$\gamma = {78^ \circ }30' $
$\alpha = {78^ \circ }30'$

$\alpha + \beta = {180^\circ } $
${78^ \circ }30' + \beta = {180^ \circ } $
$\beta = {180^ \circ } - {78^ \circ }30' $
$\beta = {101^ \circ }30' $
$\delta = {101^ \circ }30' $
${\alpha _1} = \beta $
${\alpha _1} = {101^ \circ }30' $

${\gamma _1} = {\alpha _1} $
${\gamma _1} = {101^ \circ }30' $
${\beta _1} = \alpha $
${\beta _1} = {78^ \circ }30' $
${\delta _1} = {\beta _1} $
${\delta _1} = {78^ \circ }30' $