$\text{a) Trên nửa mặt phẳng bờ chứa tia Ox có:}$
$\left \{ {{\widehat{xOy}=50^{o}(gt)} \atop {\widehat{xOz}=180^{o}(gt)}} \right.$
$\text{⇒ $\widehat{xOy}$ < $\widehat{xOz}$}$
$\text{⇒ Oy nằm giữa Ox và Oz}$
$\text{⇒ $\widehat{xOy}$ + $\widehat{yOz}$ = $\widehat{xOz}$}$
$\text{⇒ $50^{o}$ + $\widehat{yOz}$ = $180^{o}$}$
$\text{⇒ $\widehat{yOz}$ = $180^{o}$ - $50^{o}$}$
$\text{⇒ $\widehat{yOz}$ = $130^{o}$}$
$\text{Có: Ot là tia p/g của $\widehat{xOy}$ (gt)}$
$\text{⇒ $\widehat{tOy}$ = $\dfrac{\widehat{xOy}}{2}$ = $\dfrac{50^{o}}{2}$ = $25^{o}$}$
$\text{Có: $\widehat{tOy}$ + $\widehat{yOm}$ = $\widehat{tOm}$}$
$\text{⇒ $25^{o}$ + $\widehat{yOm}$ = $90^{o}$}$
$\text{⇒ $\widehat{yOm}$ = $90^{o}$ - $25^{o}$}$
$\text{⇒ $\widehat{yOm}$ = $65^{o}$}$
$\text{b) Có: $\widehat{yOm}$ + $\widehat{mOz}$ = $\widehat{yOz}$}$
$\text{⇒ $65^{o}$ + $\widehat{mOz}$ = $130^{o}$}$
$\text{⇒ $\widehat{mOz}$ = $130^{o}$ - $65^{o}$}$
$\text{⇒ $\widehat{mOz}$ = $65^{o}$}$
$\text{⇒ $\widehat{mOz}$ = $\widehat{yOm}$ (= $65^{o}$)}$
$\text{mà Om nằm giữa Oz và Oy}$
$\text{⇒ Om là tia p/g $\widehat{yOz}$}$
