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

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#### Solution

It can be observed that,

*x + y + z + w* = 360º ....(Complete angle)

It is given that,

*x + y = z + w*

∴ *x + y + x + y* = 360º

2(*x + y*) = 360º

*x + y* = 180º

Since *x* and *y* form a linear pair, AOB is a line.

Concept: Pairs of Angles

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