Marinada '24

[lang=hr] Neka je $ABC$ šiljastokutan trokut u kojem je $\angle BAC = 72^\circ$, $\angle CBA = 59^\circ$, $\angle ACB = 49^\circ$. Neka je $P$ polovište stranice $BC$, a $M$ i $N$ redom nožišta visina iz vrhova $B$ i $C$. Odredite veličinu $\angle MPN$ u stupnjevima. [/lang] [lang=en] Let $ABC$ be an acute-angled triangle where $\angle BAC = 72^\circ$, $\angle CBA = 59^\circ$, and $\angle ACB = 49^\circ$. Let $P$ be the midpoint of side $BC$, and let $M$ and $N$ be the feet of the altitudes from vertices $B$ and $C$, respectively. Determine the measure of $\angle MPN$ in degrees. [/lang]