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°.

Question

If two straight lines intersect each other in such a way that one of the angles formed measure 90&#xB0;, show that each of the remaining angles measures 90&#xB0;.

Philoid · Accepted Answer

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°.