Đáp án+Giải thích các bước giải:

$a) \Delta ABC, \widehat{BAC}+\widehat{ABC}+\widehat{ACB}=180^\circ\\ \Rightarrow \widehat{ABC}+\widehat{ACB}=180^\circ-\widehat{BAC}\\ \Leftrightarrow \dfrac{1}{3}\widehat{ACB}+\widehat{ACB}=180^\circ-60^\circ\\ \Leftrightarrow \dfrac{4}{3}\widehat{ACB}=120^\circ\\ \Leftrightarrow \widehat{ACB}=90^\circ\\ \widehat{ABC}=\dfrac{1}{3}\widehat{ACB}=30^\circ$

$b) \widehat{ABx}$ kề bù với $\widehat{ABC}$

$\Rightarrow \widehat{ABx}+\widehat{ABC}=180^\circ\\ \Rightarrow \widehat{ABx}=180^\circ-\widehat{ABC}=180^\circ-30^\circ=150^\circ$

$c) By$ là phân giác $\widehat{ABx}$

$\Rightarrow \widehat{B_1}=\widehat{B_2}=\dfrac{\widehat{ABx}}{2}=75^\circ$

$\widehat{B_1}$ kề bù với $\widehat{ABM}$

$\Rightarrow \widehat{B_1} + \widehat{ABM}=180^\circ\\ \Rightarrow  \widehat{ABM}=180^\circ-\widehat{B_1}=105^\circ\\ \Delta ABM, \widehat{ABM}+\widehat{AMB}+\widehat{BAM}=180^\circ\\ \Rightarrow  \widehat{AMB}=180^\circ-(\widehat{BAM}+\widehat{ABM})=15^\circ.$