Co-interior angles: The interior angles that lie between two lines and on the same side of a transversal are called co-interior angles. If the two lines are parallel, then co-interior angles add to give  and so are supplementary.

In the figure, the following pairs of angles are called pairs of consecutive interior angles:

Theorem: If the transversal intersects two parallel lines, then each pair of co-interior angles are supplementary.

Given: m and n are parallel lines and the transversal l cuts m and n

To Prove : 

Proof: line m and l intersect each other therefore

 Line m and n are parallel and the transversal l cuts them.

From Eq. (1) and (2)

Hence Proved that co-interior angles are supplementary.

Theorem: If a transversal intersects two lines such that a pair of co-interior angles are supplementary, then the lines are parallel

Given: m and n are lines and the transversal l cuts m and n and 

To Prove:  m and n are parallel

Proof: line m and l intersect each other therefore

 and

From Eq. (1) and (2)

But they are alternate interior angles when the transversal l cuts the line m and n

Since they are equal the lines are parallel.

Hence Proved that the lines are parallel.

Illustration: Identify co - interior angles from the given figure:

Solution: <3 and <5 are co - interior <3 + <5 = 180.

<4 and <6 are co - interior and  <4 + <6 = 180. because AB and CD are two parallel lines and a transversal L intersects them:

The converse of each of the above statements is also true.

Solution: As co-interior angles are supplementary

5x + 37 + 43 = 180 

5x =180-80

5x=100

x = 20