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

1.	In figure 6.16,if x + y=w + z, then prove that AOB is a line.
Answer» x + y = w + z . . . .[Given] . . . (1)As the sum of all angles round a point is equal to 360o{tex}\\therefore{/tex}\xa0x + y + w + z = 360o{tex}\\therefore{/tex}\xa0x + y + x + y = 360o{tex}\\therefore{/tex}\xa02(x + y) = 360o{tex}\\therefore{/tex}\xa0{tex}x+y={360^0\\over2}{/tex}{tex}\\therefore{/tex}\xa0x + y = 180o{tex}\\therefore{/tex}\xa0AOB is a line.

Discussion