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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.

Two diagrams. In each, two lines cut by tranversal EF with one pair of co-interior angles marked on each.

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.

Pair of parallel lines AB and CD cut by transversal EF intersecting at H and G. Angles AHF and EGD marked.

\(\angle\)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.

Pair of parallel lines AB and CD cut by transversal EF intersecting at H and G.

Solution

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