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°.
Find the angle θ in the diagram.
θ = 180° – 95° (co-interior angles AB || CD) = 85°