Question

Fig. 6.15
4. In Fig. 6.16, if x + y =w+z, then prove that AOB
is a line.
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Answer 1

Answer:

X + y will be on same line so there linear pair will be off 180 degree

same as w+z also will be on same line so there linear pair will be of 180 degree

as they both Are linear pair so so this AOB will be a line

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Answer 2

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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