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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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