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