To properly label the four angles, we will use the following notations:
- Let angle A be denoted as ∠AOB.
- Let angle B be denoted as ∠BOC.
- Let angle C be denoted as ∠COD.
- Let angle D be denoted as ∠DOE.
Given that A, O, and E fall on a straight line, angle A, angle B, and angle E must add up to a straight angle (180 degrees). Therefore, we have:
∠AOB + ∠BOC + ∠COD = 180 degrees.
Note that since angle A and angle E both subtend the same arc, they are vertical angles and are congruent (have equal measures):
∠AOB = ∠DOE.
Using this information, we can properly label the four angles as follows:
- The angle between rays OA and OB is ∠AOB.
- The angle between rays OB and OC is ∠BOC.
- The angle between rays OC and OD is ∠COD.
- The angle between rays OD and OE is ∠DOE, which is equal to ∠AOB.