In figure, if x + y = w + ⇒, then prove that AOB is a line.
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As Given, x+y=w+z
To Prove: AOB is a line or x+y=180°(linear pair.)
According to the question,
x+y+w+z=360°
Angles around a point.
(x+y)+(w+z)=360°
(x+y)+(x+y)=360°
Given x+y=w+z
2(x+y)=360°
(x+y)=180°
Hence, x+y makes a linear pair.
Therefore, AOB is a straight line.
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