In Fig. 6.28, find the values of x and y and then show that AB || CD.

Line CD is intersecting with line P. Hence the vertically opposite angles so formed are equal.

Thus, y = 130°.

Similarly, line AB is intersecting with line P forming a linear pair. Hence the sum of adjacent angles formed is 180°.

x + 50° = 180°

x = 180° - 50°

x = 130°

We know that, if a transversal intersects two lines such that a pair of alternate interior angles are equal, then the two lines are parallel.

Here we can see that the pair of alternate angles formed when lines AB and CD are intersected by transversal P are equal.

i.e, x = y = 130°. So we can say the two lines AB and CD are parallel.

Hence AB || CD is proved.