Question

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

Answer 1

Here is your answer! ! !

angle x + y + w + z = 360 ( angle at a point )
x + y + x + y = 360 ( given that x + y = w + z)
2 x + 2 y = 360
2 ( x + y ) = 360
x + y = 180

If x + y = 180 than Line AOB is 180 degree. Than it is a line.


I hope its helpfull for you.



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Answer 2

Given:-X+Y=W+Z

To Prove:- AOB is a line

Proof:-

as we know some of all angles around a fixed point is 360°

∠AOC+∠BOC+∠BOD+∠AOD=360°

-->Y+X+W+Z=360°

-->X+Y+X+Y=360°(∵X+Y=W+Z)

∵2(X+Y)=360°

--->X+Y=180°

THIS SHOWS THAT IT IS A LINEAR PAIR .

AND WE KNOW THAT SUM OF ALL ANGLES ON A LINE IS 180°.

HENCE , PROVED.