Question

In the given figure, if x + y = w + z, then prove that AOB is a line.

Answer 1

Given: x + y = w + z

To prove: AOB is a straight line.

Proof: x + y + w + z = 360°

or x + y + x + y = 360°

⇒ 2x + 2y = 360°

⇒ 2(x + y) = 360°

⇒ x + y = 180°    ...(Linear pair)

When the sum of two adjacent angles is 180°, then the line is straight and straight.

Hence, AOB is a line.