Lời giải:
Vì $Om$ là tia phân giác $\widehat{xOy}$ nên $\widehat{mOy}=\frac{1}{2}\widehat{xOy}$
Vì $On$ là tia phân giác $\widehat{yOz}$ nên $\widehat{yOn}=\frac{1}{2}\widehat{yOz}$
$\Rightarrow \widehat{mOy}+\widehat{yOz}=\frac{1}{2}(\widehat{xOy}+\widehat{yOz})$
$\widehat{mOn}=\frac{1}{2}.180^0$
$\widehat{mOn}=90^0$
$\Rightarrow Om\perp On$
Ta có: \(\widehat{yOm}=\dfrac{\widehat{xOy}}{2}\)
\(\widehat{yOn}=\dfrac{\widehat{zOy}}{2}\)
Do đó: \(\widehat{yOm}+\widehat{yOn}=\dfrac{\widehat{xOy}}{2}+\dfrac{\widehat{yOz}}{2}\)
\(\Leftrightarrow\widehat{mOn}=\dfrac{180^0}{2}=90^0\)(đpcm)
