a) $\widehat{xOy}=m^o$, $\widehat{yOz}=n^o$
mà $Oy$ nằm giữa $Ox,Oz$
$→\widehat{xOz}m^o+n^o$
mà $Om$ là phân giác $\widehat{xOz}$
$→\widehat{xOm}=\dfrac{m^o+n^o}{2}$
Tính $\widehat{yOm}$
Xét TH1: Nếu $\widehat{xOm}>\widehat{xOy}$
$→Oy$ nằm giữa $Om,On$
$→\widehat{xOy}+\widehat{yOm}=\widehat{xOm}$
$→\widehat{yOm}=\widehat{xOm}-\widehat{xOy}=\dfrac{m^o+n^o}{2}-m^o=\dfrac{m^o+n^o-2n^o}{2}=\dfrac{m^o-n^o}{2}$
Xét TH2: Nếu $\widehat{xOm}<\widehat{xOy}$
$→Om$ nằm giữa $Ox,Oy$
$→\widehat{xOm}+\widehat{yOm}=\widehat{xOy}$
$→\widehat{yOm}=\widehat{xOy}-\widehat{xOm}=m^o-\dfrac{m^o+n^o}{2}=\dfrac{2m^o-m^o+n^o}{2}=\dfrac{m^o+n^o}{2}$
b) $Ot'$ là phân giác $\widehat{yOz}$
mà $Ot$ là phân giác $\widehat{xOy}$
$→\widehat{tOt'}=\dfrac{\widehat{yOz}}{2}+\dfrac{\widehat{xOy}}{2}=\dfrac{m^o+n^o}{2}$
mà $\widehat{xOm}=\dfrac{m^o+n^o}{2}$
$→\widehat{tOt'}=\widehat{xOm}$
