Given that,
The rays OA, OB, OC, OD, and OE have the common endpoint O.
A ray of opposite to OA is drawn.
Since,
∠AOB, ∠BOF are linear pair
∠AOB + ∠BOF = 180°
∠AOB + ∠BOC + ∠COF = 180° (i)
Also,
∠AOE + ∠EOF = 180°
∠AOE + ∠DOF + ∠DOE = 180° (ii)
Adding (i) and (ii), we get
∠AOB + ∠BOC + ∠COF + ∠AOE + ∠DOF + ∠DOE = 360°
∠AOB + ∠BOC + ∠COD + ∠DOE + ∠EOA = 360°
Hence, proved