( 1)

∫OB direction is 40 north by west, and OA direction is15 north by east.

∴∠NOB=40，∠NOA= 15，

∴∠AOB=∠NOB+∠NOA=55，

∠∠AOB =∠AOC，

∴∠AOC=55，

∴∠NOC=∠NOA+∠AOC=70，

∴ The direction of OC is 70 east by north.

(2)

∠∠AOB = 55, OA is the bisector of∠∠ BOC.

∴∠AOB=∠AOC

∴∠AOC=55

∫ Ray OD is the reverse extension ray OD of OB.

The degree to the south of ray OD is 40 degrees (the vertex angles are equal).

∴∠cod= 180- 15-55-40 = 70

(3)

∫OE aliquot ∠COD

∴∠COE= 1/2∠COD=35

∴∠AOE=∠AOC+∠COE=55 +35 =90