Question -
Answer -
Given: Rays OA, OB, OC, OD and OE have the common endpoint O.
Draw an opposite ray OX to ray OA, which make a straight lineAX.
From figure:
∠AOB and∠BOX arelinear pair angles, therefore,
∠AOB +∠BOX = 1800
Or, ∠AOB + ∠BOC + ∠COX = 1800 —–—–(1)
Also,
∠AOE and∠EOX arelinear pair angles, therefore,
∠AOE+∠EOX =180°
Or, ∠AOE + ∠DOE + ∠DOX = 1800 —–(2)
By adding equations, (1) and (2), we get;
∠AOB + ∠BOC + ∠COF + ∠AOE + ∠DOE + ∠DOX = 1800 + 1800
∠AOB + ∠BOC + ∠COD + ∠DOE + ∠EOA = 3600
Hence Proved.