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Question

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


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Solution

Prove the given statement

The sum of all angles around a point is 360

Consider the point O

The sum of all angles around O must be 360

COA+COB+AOD+DOB=360

x+y+w+z=360

2(x+y)=360 [x+y=w+z]

x+y=180

The sum of angles across AOB is thus 180 thereby making it a straight line

Hence it is proved that AOB is a straight line.


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