$Đáp$ $án$ $+$ $Giải$ $thích$ $các$ $bước$ $giải$ $:$

$a)$ $Ta$ $có$ `\hat{xOm} + \hat{mOy} = 180^o` $($ $kề$ $bù$ $)$

                  $\Longrightarrow$ `30^o + \hat{mOy} = 180^o`

                  $\Longrightarrow$ `\hat{mOy} = 180^o - 30^o`

                  $\Longrightarrow$ `\hat{mOy} = 150^o`

  $Do$ $Ot$ $là$ $phân$ $giác$ `\hat{mOy}` $.$

$\Longrightarrow \begin{cases} \widehat{mOt} = \widehat{tOy} = \dfrac{1}{2}\widehat{mOy }\end{cases}$

$\Longrightarrow \begin{cases} \widehat{tOy} = \dfrac{1}{2}\ \times 150^o \end{cases}$

$\Longrightarrow \begin{cases} \widehat{tOy} = 75^o \end{cases}$

 $Vậy$ `\hat{tOy} = 75^o`

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$b)$ $Do$ $Om$ $là$ $phân$ $giác$ `\hat{xOy}` $.$

$\Longrightarrow \begin{cases} \widehat{xOm} = \widehat{mOy} = \dfrac{1}{2}\widehat{xOy} \end{cases}$

$\Longrightarrow \begin{cases} \widehat{mOy} = \dfrac{1}{2} \times 120^o \end{cases}$

$\Longrightarrow \begin{cases} \widehat{mOy} = 60^o \end{cases}$

   $Do$ $On$ $là$ $phân$ $giác$ $\widehat{mOy}$ $.$

$\Longrightarrow \begin{cases} \widehat{mOn} = \widehat{nOy} = \dfrac{1}{2}\widehat{mOy} \end{cases}$

$\Longrightarrow \begin{cases} \widehat{mOn} = \dfrac{1}{2} \times 60^o \end{cases}$

$\Longrightarrow \begin{cases} \widehat{mOn} = 30^o \end{cases}$

   $Vậy$ `\hat{mOn} = 30^o`