Question

If x + y =w+z then prove that AOB is a line.

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Answer 1

$as \: givan. \: x + y = w + z \\ \\ to \: prove. \: aob \: is \: a \: line \: or \: x + y = 180 \\ according \: to \: question \: . \\ x + y + w + z = 360(angl \: around \: a \: point) \\ (x + y) + (w + z) = 360(given = x+ y = w + z \\ \\ 2(x + y) = 360 \\ ( x+y ) = \frac{360 }{2} \\ ( x+ y) = 180 \\ hence. \: x + y \: makes \: a \: linear \: pair \\ therefore \: .aob \: is \: a \: straight \: line..$

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Answer 2

Question :-

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

Answer :-

Sum of all the angles at a point = 360°

∴ x + y + ⇒ + w = 360° or, (x + y) + (⇒ + w) = 360°

But (x + y) = (⇒ + 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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