[tex]a)m(\measuredangle BOC)=360^{\circ}-120^{\circ}-90^{\circ}-90^{\circ}=\boxed{60^{\circ}.}\\
b)Fie~(OM-bis.(\measuredangle BOC)~si~(ON-bis.(\measuredangle AOD). \\ m(\measuredangle MON)= \frac{120^{\circ}}{2}+90^{\circ}+ \frac{60^{\circ}}{2}=60^{\circ}+90^{\circ}+30^{\circ}=\boxed{180^{\circ}.}[/tex]