In parallelogram LOST, SN Ol and SM LT. Find STM, SON and NSM.
∠S + ∠T + ∠M = 180
40 + ∠STM + 90 = 180
∠STM = 180-130 = 50
∠STM = ∠SON (these are opposite angles).
∠SON = 50
∠SON and ∠OST are adjacent angles.
⟹Hence, ∠SON + ∠NSO + ∠NSM + ∠MST = 180
50 + (180-(90 + 50)) + ∠NSM + 40 = 180
∠NSM = 140-90
∠NSM = 50
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