Q6 of 12 Page 84

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

In a circle, the sum of all angles is 360°


∴ ∠AOC + ∠BOC + ∠DOB + ∠AOD = 360°


⇒ x + y + w + z = 360°


Given that, x + y = w + z


⇒ w + z + w + z = 360°


⇒ 2w + 2z = 360°


⇒ 2(w + z) = 360°


⇒ w + z = 180° or ∠DOB + ∠AOD = 180°


If the sum of two adjacent angles is 180° then it forms a line.


So AOB is a line.


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