Two angles that end at the same ray
4.16 If angles α and β are in standard position on the coordinate plane and are coterminal, what can you conclude about α and β? Can you conclude that α and β have the same measure? Why or why not?
If two angles in standard position are coterminal, their terminal sides coincide. In other words, their terminal sides lie on the same ray. Recall that the angles are in standard position, so their initial sides coincide as well; both initial sides lie along the positive x-axis. Although angles α and β have a great deal in common, you cannot conclude that they have the same measure.
Just because two angles begin and end at the same ray, they may differ in the direction or in the number of rotations ...