Determine if triangles are congruent

Dear Student,
angle OQN=180-50-50=80 (Sum Of Angles In Triangle is 180)
Considering the point in the centre to be point Q,
angle OQN + angle NQM=180(Angles in Linear Pair)
Thus, angle NQM= 180-80=100
Similarly, angle QPO= angle MNQ = 40(Alternate Angles)
angle OQN + angle OQP=180 (Angles in Linear Pair)
angle OQP= 180-80=100
Also, angle QOP = 180-40-100=40
Thus triangles QMN and QOP are congruent.
Regards.