Q. 205.0( 2 Votes )

Rays OA, OB, OC, OD

Answer :

Given: OA, OB, OC, OD and OE have common end point O.
To prove: ∠ AOB + ∠ BOC+ ∠ COD + ∠ DOE + ∠ EOA = 360°.
Construction: Draw the ray opposite to OA.
Proof: Adjacents, ∠COF and ∠COA form a linear pair.
⇒ ∠COF + ∠COA = 180°     (Linear Pair Axiom) --------------(1)
Similarly, adjacents,  ഏOD and ∠DOA form a linear pair.
⇒ ∠FOD + ∠DOA = 180°                              --------------- (2) 
Adding (1) and (2)
                            ∠COF + ∠COA + ∠FOD + ∠DOA  = 180° + 180°
(∠COF + ∠FOD) + ∠COB + ∠BOA + (∠EOA + ∠DOE)  = 360°
            ∠ AOB + ∠ BOC+ ∠ COD + ∠ DOE + ∠ EOA = 360°.

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