Question

In Fig 6.16, if x+y=w+z, then prove that AOB is a line.​

Answer 1

Solution

Sum of all angles in a circle always 360°

Hence

∠AOC + ∠BOC + ∠DOB + ∠AOD = 360°

=> x + y + w + z = 360°

=> x + y + x + y = 360°

Given that x + y = w + z

Plug the value we get

=> 2w + 2z = 360°

=> 2(w + z) = 360°

w + z = 180° (linear pair)

or ∠BOD + ∠AOD = 180°

If the sum of two adjacent angles is 180°, then the non-common arms of the angles form a line

Hence AOB is a line.

Answer 2

Hope it is helpful........