Question

If a transversal intersects two parallel lines ,then prove that each pair of consecutive interior angles is supplementary.

Answer 1

Answer:

Given:

Line l and m are parallel lines.

line n is a traversal line for l and m.

To Prove: Each pair of consecutive interior angles is supplementary that is ∠1 + ∠2 = 180°

We know that when line are parallel then Alternate interior angles are equal.

So,

∠1 = ∠3 ...............................(1)

Now, from figure,

∠2 + ∠3 = 180° ( linear pair ) ........................(2)

From (1) and (2),

∠1 + ∠2 = 180°

Hence Proved.