$\widehat{tOy}=\widehat{zOt}+\widehat{yOz}$
$\widehat{xOz}=\widehat{zOt}+\widehat{xOt}$
$\to \widehat{zOt}+\widehat{yOz}+\widehat{zOt}+\widehat{xOt}=180^\circ$
$\to (\widehat{yOz}+\widehat{zOt}+\widehat{xOt})+\widehat{zOt}=180^\circ$
$\to \widehat{xOy}+\widehat{zOt}=180^\circ$