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

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

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Given that,
$x+y = z+w$..............(i)
It is known that, the sum of all the angles at a point = $360^0$
$\therefore$  $x+y+z+w=360^0$..............(ii)

From eq (i) and eq (ii), we get

$\\2(x+y)=360^0\\ x+y = 180^0$

Hence proved AOB is a line.

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