Let $ABC$ be a triangle and $O$ the center of its enscribed circle.
Let $M = BO \cap AC$ and $N=CO \cap AB$ such that $\measuredangle NMB = 30°, \measuredangle MNC = 50°$.
Find $\angle ABC, \angle BCA$ and $\angle CAB$.
I also posted this here at the Art of Problem Solving.