a, Ta có:
$\widehat{x'Oy}$+$\widehat{xOy}$$=180^o$
⇔$120^o+$$\widehat{xOy}$$=180^o$
⇔$\widehat{xOy}$$=60^o$
Ta thấy: $\widehat{xOz}$<$\widehat{xOy}$ ($30^o<60^o$)
⇒$Oz$ nằm giữa 2 tia $Ox,Oy$
b.
Ta có:
$Oz$ nằm giữa 2 tia $Ox,Oy$
$\widehat{xOz}$=$\widehat{yOz}$=$\dfrac{1}{2}$.$\widehat{xOy}$=$\dfrac{1}{2}$.$60^o=30^o$
⇒$Oz$ là tia phân giác $\widehat{xOy}$
c,
Ta có: $Oz'$ là tia phân giác $\widehat{x'Oy}$
⇒$\widehat{yOz'}$=$\dfrac{1}{2}$.$\widehat{x'Oy}$=$\dfrac{1}{2}$.$120^o$=$60^o$
Ta có: $Oy$ nằm giữa $Oz;Oz'$
⇒$\widehat{zOy}$+$\widehat{z'Oy}$$=$$\widehat{zOz'}$
⇒$30^o+60^o=$$\widehat{zOz'}$
⇒$\widehat{zOz'}$$=90^o$