Die Winkelsumme im Dreieck beträgt ${180}^{\circ }180^\backslash circ$

$\begin{array}{c}\alpha +\beta +{100}^{\circ }={180}^{\circ }\\ \alpha +\beta ={80}^{\circ }\end{array}\backslash def\backslash arraystretch\{1.25\}\; \backslash begin\{array\}\{l\}\backslash alpha+\backslash beta+100^\backslash circ=180^\backslash circ\backslash \backslash \backslash alpha+\backslash beta=80^\backslash circ\backslash end\{array\}$

Die Summe von Nebenwinkeln beträgt ${180}^{\circ }180^\backslash circ$.

$\begin{array}{c}\alpha +\alpha \ast ={180}^{\circ }\\ \alpha ={180}^{\circ }-\alpha \ast \\ \\ \beta +\beta \ast ={180}^{\circ }\\ \beta ={180}^{\circ }-\beta \ast \end{array}\backslash def\backslash arraystretch\{1.25\}\; \backslash begin\{array\}\{l\}\backslash alpha+\backslash alpha\backslash ast=180^\backslash circ\backslash \backslash \backslash alpha=180^\backslash circ-\backslash alpha\backslash ast\backslash \backslash \backslash \backslash \backslash beta+\backslash beta\backslash ast=180^\backslash circ\backslash \backslash \backslash beta=180^\backslash circ-\backslash beta\backslash ast\backslash end\{array\}$

$\begin{array}{c}({180}^{\circ }-\alpha \ast )+({180}^{\circ }-\beta \ast )={80}^{\circ }\end{array}\backslash def\backslash arraystretch\{1.25\}\; \backslash begin\{array\}\{l\}(180^\backslash circ-\backslash alpha\backslash ast)+(180^\backslash circ-\backslash beta\backslash ast)=80^\backslash circ\backslash end\{array\}$

$\begin{array}{c}{360}^{\circ }-\alpha \ast -\beta \ast ={80}^{\circ }\\ \end{array}\backslash def\backslash arraystretch\{1.25\}\; \backslash begin\{array\}\{l\}360^\backslash circ-\backslash alpha\backslash ast-\backslash beta\backslash ast=80^\backslash circ\backslash \backslash \backslash \backslash \backslash end\{array\}$

${280}^{\circ }=\alpha \ast +\beta \ast 280^\backslash circ=\backslash alpha\backslash ast+\backslash beta\backslash ast$

Die Lösung lautet $\alpha \ast +\beta \ast ={280}^{\circ }\backslash alpha\backslash ast+\backslash beta\backslash ast=280^\backslash circ$