When two lines are cut by a transversal, the pair of angles on one side of the transversal and inside the two lines are called the consecutive interior angles.
In the figure, the angles 3 and 5 are consecutive interior angles.
Also the angles 4 and 6 are consecutive interior angles.
If two parallel lines are cut by a transversal, then the pairs of consecutive interior angles formed are supplementary.
Proof:
Given: k  l is a transversal
Prove: ∠3 and ∠5 are supplementary and ∠4 and ∠6 are supplementary.
Statement 
Reason 

1 
k  l, t is a traversal. 
Given 
2 
form a linear pair and form a linear pair. 
Definition of linear pair 
3 
are supplementary are supplementary 

4 
Corresponding Angles Theorem 

5 
are supplementary are supplementary. 
Substitution Property 