Question

In Fig., rays OA, OB, OC, OD and OE have the common endpoint, O. Show, that ∠AOB +∠BOC +∠COD +∠DOE + ∠EOA = 360°.

Answer 1

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