Mathematics

In Fig. If $$  x+y=w+z  $$ then prove that $$  A O B  $$ is a line.


SOLUTION
Given $$x+y=z+w\cdots(1)$$
From Angle at a point theorem
Sum of all angles at a point is $$360^{\circ}$$
So $$x+y+z+w=360\\x+y+x+y=360\\2(x+y)=360\\x+y=180$$
$$ x,y $$ are adjacent angles and form $$180^{\circ} $$ together so $$AOB$$ is a straight line
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