Question

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

Answer 1

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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