$\textit{Đáp án + Giải thích các bước giải:}$
$\text{Có $\widehat{M_1}$ = $\widehat{M_3}$ (đồng vị)}$
$\text{⇒ $\widehat{M_2}$ + $\widehat{M_3}$ + $\widehat{M_4}$ = $\widehat{M_1}$ + $\widehat{M_2}$ + $\widehat{M_4}$ = 180°}$
$\text{Xét ΔMCE: $\widehat{C}$ + $\widehat{E}$ + $\widehat{M_2}$ = 180°}$
$\text{Xét ΔMAF: $\widehat{A}$ + $\widehat{F}$ + $\widehat{M_1}$ = 180°}$
$\text{Xét ΔMDB: $\widehat{B}$ + $\widehat{D}$ + $\widehat{M_4}$ = 180°}$
$\text{⇒ $\widehat{C}$ + $\widehat{E}$ + $\widehat{M_2}$ + $\widehat{A}$ + $\widehat{F}$ + $\widehat{M_1}$ + $\widehat{B}$ + $\widehat{D}$ + $\widehat{M_4}$ = 3 . 180°}$
$\text{⇒ ($\widehat{C}$ + $\widehat{E}$ + $\widehat{A}$ + $\widehat{F}$ + $\widehat{B}$ + $\widehat{D}$) + ($\widehat{M_1}$ + $\widehat{M_2}$ + $\widehat{M_4}$ = 540°}$
$\text{⇒ $\widehat{C}$ + $\widehat{E}$ + $\widehat{A}$ + $\widehat{F}$ + $\widehat{B}$ + $\widehat{D}$ + 180° = 540°}$
$\text{⇒ $\widehat{C}$ + $\widehat{E}$ + $\widehat{A}$ + $\widehat{F}$ + $\widehat{B}$ + $\widehat{D}$ = 540° - 180°}$
$\text{⇒ $\widehat{C}$ + $\widehat{E}$ + $\widehat{A}$ + $\widehat{F}$ + $\widehat{B}$ + $\widehat{D}$ = 360°}$
$\text{Vậy $\widehat{C}$ + $\widehat{E}$ + $\widehat{A}$ + $\widehat{F}$ + $\widehat{B}$ + $\widehat{D}$ = 360°}$
