In triangle $ABC$, $m\measuredangle A=100^\circ$, $m\measuredangle B=50^\circ$, and $m\measuredangle C=30^\circ$. Points X and Y are on the sides of the triangle so that $\overline{AX}$ is an altitude and $\overline{BY}$ is a median. Compute $m\measuredangle YXC$.
I drew the diagram and it appears to me that $\overline{YX}$ and $\overline{AB}$ are parallel, which would give $m\measuredangle YXC=50^\circ$, but I'm not sure how to demonstrate this.
$YX$ is not parallel to $AB$. Focus on the triangle $AXC$ and compute all three of its angles. Is that a special triangle? Then what can you say about the length of $AX$, the length of $AC$ and the length of $AY$ (recall $BY$ is a median). Now, can you compute all the angles of triangle $AXY$? Consequently, how much is $\angle \, YXC$? It is not $50^{\circ}$.