Segments MN, LT, PQ, and OR all intersect at point S. If m∠LSO = m∠PSN , prove m∠LSP = m∠OSN .

Question

write a two column proof

Answer 1

Assuming that the 1st letters are in sequence around S, the angles follow
LSO=LSP+PSO
PSN=PSO+OSN
That means
LSP+PSO=PSO+OSN
so
LSP=OSN

Now just change that to a 2-column proof.