Question

If one of the four angles are formed by two intersecting lines is a right angle ,then show that each of the four angles is a right angle.

Answer 1

hope this will help you

Answer 2

Answer:

The proof is explained step-wise below :

Step-by-step explanation:

For better understanding of the solution, see the attached figure :

Let m∠AOC be 90°

⇒ m∠AOC = m∠BOD (Vertically Opposite angles are equal)

⇒ m∠BOD = 90°

Now, m∠AOB = 180° (Linear Pair is supplementary)

⇒ m∠AOC + m∠BOC = 180°

⇒ m∠BOC = 180° - 90°

⇒ m∠BOC = 90°

And, m∠BOC = m∠AOD (Vertically opposite angles are equal)

⇒ m∠AOD = 90°

Hence, m∠AOC = m∠BOC = m∠AOD = m∠BOD = 90°

Hence Proved.