Question

In Fig. 8.34, rays OA, OB, OC, OD and OE have the common endpoint, O. Show, that ∠AOB +∠BOC +∠COD +∠DOE + ∠EOA = 360°.

Answer 1

we know that on a point the angle is equal to the 360 so the sum of all angles on a point will be 360

Answer 2

Given : Rays OA, OB, OC, OD and OE have the common endpoint, O.  

To show :  ∠AOB +∠BOC +∠COD +∠DOE + ∠EOA = 360°.

Construction : Draw an opposite ray OF to ray OA, which makes a straight line AF.

From figure :  

∠AOB and ∠BOF are linear pair.

∠AOB + ∠BOF = 180°

∠AOB + ∠BOC + ∠COF = 180° ………….(i)

Also,∠EOA and ∠EOF are linear pair.

∠EOA + ∠EOF = 180°

∠EOA + ∠DOF + ∠DOE = 180° ………... (ii)

On adding eq (i) and (ii), we get :  

∠AOB + ∠BOC + ∠COF + ∠EOA + ∠DOF + ∠DOE = 360°

∠AOB + ∠BOC + (∠COF + ∠DOF) + ∠EOA + ∠DOE = 360°

∠AOB + ∠BOC + ∠COD + ∠EOA + ∠DOE = 360°

Hence, proved

HOPE THIS ANSWER WILL HELP YOU…..

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