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Proof

Given lines AB and CD intersect each other at point O and ∠AOC = 90°

∠AOC = ∠BOD (Opposite angles)

Therefore, ∠BOD = 90°

⇒ ∠BOD + ∠AOC = 180°

⇒ ∠BOC + 90° = 180°

⇒ ∠BOC = 90°

Now, ∠AOD = ∠BOC (Opposite angles)

Therefore,

∠AOD = 90°

Proved each of the remaining angles measures 90°.