Math, asked by tumpadas1984, 11 months ago

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Answered by capabilitymister
2

Given : 4 rays OA, OB, OC and OD.

To Prove : ∠AOC + ∠COB + ∠BOD + ∠AOD = 360°

Const : Extend line OA to form another ray OM

Proof : ∠AOD + ∠DOM = 180°    (AOM is a line) _______(i)

and, ∠AOC + ∠COB + ∠BOM = 180°    (AOM is a line)________(ii)

Adding (i) and (ii)

∠AOC + ∠COB + ∠BOM + ∠AOD + ∠DOM = 360°

∠AOC + ∠COB + ∠BOD + ∠AOD = 360°

Hence Proved

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