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