Prove that: vertically opposite angles are equal.

1.	Prove that: vertically opposite angles are equal.
Answer» let AB and CD be two lines intersecting at O . They lead to two pairs of vertically opposite angles, namely,(i) ∠ AOC and ∠ BOD (ii) ∠ AOD and ∠ BOC.We need to prove that ∠ AOC = ∠ BOD and ∠ AOD = ∠ BOC.Now, ray OA stands on line CD.Therefore, ∠ AOC + ∠ AOD = 180° (Linear pair axiom) ………..(1)We can write ∠ AOD + ∠ BOD = 180° (Linear pair axiom)……………(2)From (1) and (2), we can write∠ AOC + ∠ AOD = ∠ AOD + ∠ BODThis implies that ∠ AOC = ∠ BOD Therefore it is proved lines intersect each other then the vertically opposite angles are equal\u200b. Yes

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