In Fig. 6.28, fin

From the figure:

x + 50o = 180o (Linear pair)

x = 180- 50o

x = 130o

And,

y = 130o (Vertically opposite angles)

Now,

x = y = 130o (Alternate interior angles)

Hence,

The theorem says that when the lines are parallel, that the alternate interior angles are equal. And thus the lines must be parallel.

AB || CD

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