Question

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

Answer 1

Answer:

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Answer 2

As Given,

$x + y = w + z$

To Prove: AOB is a line or

$x + y = 180 ^{o}$

(linear pair.)

According to the question,

$x + y + w + z \: = 360^{o}$

(Angles around a point.)

$(x + y) + (w + z) = {360}^{o}$

$(x + y) + (x + y) = {360}^{o}$

(Given)

$2(x + y) = {360}^{o}$

$(x + y) = {360}^{o} \div 2$

$(x + y) = {180}^{o}$

Hence, x + y makes a linear pair.

Therefore, AOB is a straight line.

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