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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Subjective Medium Published on 09th 09, 2020
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