5. In a triangle $L M N$ the angles at vertices $L$ and $N$ have measures, respectively, $42^{\circ}$ and $80^{\circ}$. Let $r$ be the line passing through $M$ that is perpendicular to the bisector of the angle $\widehat{L M N}$ and let $O$ be the point of intersection between $r$ and the line $L N$. What is the measure of the angle $\widehat{M O N}$?
(A) $17^{\circ}$
(B) $15^{\circ}$
(C) $18^{\circ}$
(D) $21^{\circ}$
(E) $19^{\circ}$
(5) The correct answer is $(E)$.

In the triangle $M O N$, the angles at vertices $M$ and $N$ measure, respectively, $61^{\circ}$ and $100^{\circ}$. The angle at $O$ therefore measures $180^{\circ}-\left(61^{\circ}+100^{\circ}\right)=19^{\circ}$.

Question proposed by Carlo Cassola.