Sum of angles of a quadrilateral is 360°

In the quadrilateral MPNO

∠NOP = 45°, ∠OMP = ∠PNO = 90°,

Let angle ∠MPN is x°

∠NOP + ∠OMP + ∠PNO + ∠MPN = 360°

45° + 90° + 90° + x° =

x° =

x° = 135°

Therefore ∠MPN is 135°