Die Winkelsumme im Dreieck $=180\mathrm{°}=180°$

$120\mathrm{°}+\alpha 120°+\backslash alpha\backslash$und$100\mathrm{°}+\gamma \backslash \; 100°+\backslash gamma\backslash$bilden einen gestreckten Winkel.

$\beta +100\mathrm{°}=180\mathrm{°}\Rightarrow \beta =180\mathrm{°}-100\mathrm{°}=80\mathrm{°}\backslash \; \backslash beta+100°=180°\backslash Rightarrow\backslash beta=180°-100°=80°$

$\gamma +120\mathrm{°}=180\mathrm{°}\Rightarrow \gamma =180\mathrm{°}-120\mathrm{°}=60\mathrm{°}\backslash \; \backslash gamma+120°=180°\; \backslash Rightarrow\backslash gamma=180°-120°=60°$

$\alpha +\beta +\gamma =180\mathrm{°}\Rightarrow \alpha =180\mathrm{°}-\beta -\gamma \Rightarrow \alpha =180\mathrm{°}-80\mathrm{°}-60\mathrm{°}\backslash \; \backslash alpha+\backslash beta+\backslash gamma=180°\backslash Rightarrow\backslash alpha=180°-\backslash beta-\backslash gamma\backslash Rightarrow\backslash alpha=180°-80°-60°$

$\alpha =40\mathrm{°}\backslash \; \backslash alpha=40°$

Der Winkel$\alpha \backslash \; \backslash alpha\backslash$beträgt $40\mathrm{°}\backslash \; 40°$