Question

x+y=w+z proof that AOB is a line​

Answer 1

Answer:

As Given, x+y=w+z

To Prove: AOB is a line or x+y=180∘ (linear pair.)

According to the question,

x+y+w+z=360∘ ∣ Angles around a point.

(x+y)+(w+z)=360∘

(x+y)+(x+y)=360∘ ∣ Given x+y=w+z

2(x+y)=360∘

(x+y)=180∘

Hence, x+y makes a linear pair. 

Therefore, AOB is a straight 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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