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In fig.6.16, if x+y=w+z, then prove …

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

Posted by Adarsh Sharma 4 years, 9 months ago

CBSE > Class 09 > Mathematics

1 answers

Mehak ❤️ 4 years, 9 months ago

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.

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CBSE > Class 09 > Mathematics