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In Fig. 6.16, if x+y=w+z, then prove tha...

In Fig. 6.16, if `x+y=w+z`, then prove that AOB is a line.

Text Solution

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`angleBOC+angleCOA+angleAOD+angleDOB=360^@`
x+y+z+w=`360^@`
(x+y)+(w+z)=`360^@`
(x+y)=(w+z)=`180^@`non common arms of angles forms a line
putting this value in equation (1)
2(x+y)=`360^@`
(x+y)=`180^@`
so, AOB is a line.
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