$\text{a) Có: OQ nằm giữa OM và ON (gt)}$
$\text{⇒ $\widehat{MOQ}$ + $\widehat{QON}$ = $\widehat{MON}$}$
$\text{⇒ $\widehat{MOQ}$ = $\widehat{MON}$ - $\widehat{QON}$}$
$\text{⇒ $\widehat{MOQ}$ = $140^{o}$ - $90^{o}$ = $50^{o}$ (1)}$
$\text{Có: OP nằm giữa OM và ON (gt)}$
$\text{⇒ $\widehat{MOP}$ + $\widehat{PON}$ = $\widehat{MON}$}$
$\text{⇒ $\widehat{PON}$ = $\widehat{MON}$ - $\widehat{MOP}$}$
$\text{⇒ $\widehat{PON}$ = $140^{o}$ - $90^{o}$ = $50^{o}$ (2)}$
$\text{từ (1), (2) ⇒ $\widehat{MOQ}$ = $\widehat{PON}$ (= $50^{o}$)}$
$\text{b) Có: $\widehat{MOQ}$ + $\widehat{POQ}$ + $\widehat{PON}$ = $\widehat{MON}$}$
$\text{⇒ $\widehat{POQ}$ = $\widehat{MON}$ - $\widehat{MOQ}$ - $\widehat{PON}$}$
$\text{⇒ $\widehat{POQ}$ = $140^{o}$ - $50^{o}$ - $50^{o}$ = $40^{o}$}$
