4. In Fig. 6.16. if x+y=w+z, then prove that AOB is a line.
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Question :-
In figure, if x + y = w + z, then prove that AOB is a line.
Answer :-
Sum of all the angles at a point = 360°
∴ x + y + z + w = 360° or, (x + y) + (z + w) = 360°
But (x + y) = (z + w) [Given]
∴ (x + y) + (x + y) = 360° or,
2(x + y) = 360°
or, (x + y) = 360° /2 = 180°
∴ AOB is a straight line.
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