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: $k\parallel l$, $t$ is a transversal
Prove: $\angle 3$ and $\angle 5$ are supplementary and $\angle 4$ and $\angle 6$ are supplementary.
Statement 
Reason 

1 
$k\parallel l$, $t$ is a traversal. 
Given 
2 
$\angle 1$ and $\angle 3$ form a linear pair and $\angle 2$ and $\angle 4$ form a linear pair. 
Definition of linear pair 
3 
$\angle 1$ and $\angle 3$ are supplementary $m\angle 1+m\angle 3=180\xb0$ $\angle 2$ and $\angle 4$ are supplementary $m\angle 2+m\angle 4=180\xb0$ 

4 
$\angle 1\cong \angle 5$ and $\angle 2\cong \angle 6$ 
Corresponding Angles Theorem 
5 
$\angle 3$ and $\angle 5$ are supplementary $\angle 4$ and $\angle 6$ are supplementary. 
Substitution Property 