Was the search of the briefcase valid? Justify your answers

Highway patrol officer X stopped a vehicle on the freeway for speeding.  Prior to issuing a ticket for speeding, Officer X looked around the car and asked the driver to open the glove compartment.  The driver voluntarily complied.  Drugs were found in the glove compartment.  Officer X then arrested the driver and searched the whole car, including a briefcase marked “private” that was found in the trunk of the car.

Was the search of the trunk valid?

Was the search of the briefcase valid?  Justify your answers