### Co-interior angles

In each diagram below, the two marked angles are **co-interior angles** because they are between the two lines and on the same side as the transversal *EF*.

### Co-interior angles and parallel lines

If the lines are parallel, then the sum of the co-interior angles is 180°.

They are **supplementary angles**.

This can be proven using the earlier results.

\(\angle\)AHF = \(\angle\)EGD (alternate angles AB || CD)

\(\angle\)CGF + \(\angle\)EGD = 180° (straight angle at G)

Hence \(\angle\)AHF + \(\angle\)CGF = 180°.

#### Example 3

Find the angle θ in the diagram.

#### Solution

θ = 180° – 95° (co-interior angles *AB* || *CD)* = 85°