The angle J formed from the two secants is half the difference of the subtended arcs, J = (1/2) (arc PN - arc KL).
30 = (1/2) (81 - KL)
60 = 81 - KL
KL = 81 - 60 = 21 degrees
The two vertical angles, OMP and KML, add up to the two subtended arcs, KL and OP. Since the vertical angles are congruent,
2 ∠OMP = 57 + 21 = 78
Answer: ∠OMP = 39 degrees
