In the figure join O and P,
dividing the angle AOB into two parts ,namely Angle MOP=x , Angle NOP=40-x
in rt angled triangle AOP,where MOP=40-x ,OMP= 90 ,OPM= y(lets assume)
40-x + 90 + y =180 ---->(1)
in rt angled triangle AOP,where NOP=x ,ONP= 90 ,OPN= z(lets assume)
x + 90 + z =180 ------>(2)
Adding equations (1) and (2)
x+90+z +40-x +90 +y =360
y + z + 220 = 360
y + z = 140
since y + z =MPN
angle MPN =140