Die Winkel $\alpha \backslash alpha$ und der Winkel ${50}^{\circ }50^\{\backslash circ\}$ sind Wechselwinke, Wechselwinkel (auch Z-Winkel genannt) an parallelen Geraden sind gleich groß.

Also ist: $\alpha ={50}^{\circ }\backslash alpha\backslash \; =\backslash \; 50^\{\backslash circ\}$

Da die Winkelsumme im Dreieck ${180}^{\circ }180^\{\backslash circ\}$ beträgt ist:

$\alpha +\beta +{70}^{\circ }={180}^{\circ }\Rightarrow \beta ={180}^{\circ }-{70}^{\circ }-{50}^{\circ }={60}^{\circ }\backslash alpha\backslash \; +\backslash \; \backslash beta\backslash \; +\backslash \; 70^\{\backslash circ\}\backslash \; =\backslash \; 180^\{\backslash circ\}\backslash quad\backslash Rightarrow\backslash quad\backslash beta\backslash \; =\backslash \; 180^\{\backslash circ\}\backslash \; -\backslash \; 70^\{\backslash circ\}\backslash \; -\backslash \; 50^\{\backslash circ\}\backslash \; =\backslash \; 60^\{\backslash circ\}$

$\beta ={60}^{\circ }\backslash beta\backslash \; =\backslash \; 60^\{\backslash circ\}$