If two straight lines intersect each other in such a way that one of the angles formed measure 90°, show that each of the remaining angles measures 90°.
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°.