Co-interior Angles | Moosa Academy

Not every pair of angles around a transversal is equal. Co-interior angles — the interior pair on the same side of the transversal — behave differently: they add to 180°. Keeping them apart from alternate interior angles, which are equal, is the whole skill here.

Concept What they are

Co-interior angles are the interior angles trapped between two lines and lying on one side of the transversal.

The pairs are

(3,\ 6)

and

(4,\ 5)

Both angles of each pair are interior, and both sit on the same side of the transversal.

Concept The rule

\angle 3 + \angle 6 = 180° \qquad \angle 4 + \angle 5 = 180°

Angles that sum to 180° like this are supplementary. As one grows the other must shrink by the same amount, so the total never changes.

As with the other named pairs, this holds only when the two lines are parallel.

Example Finding the partner angle

Two parallel lines are cut by a transversal, and $\angle 3 = 55°$ . Find $\angle 6$ .

Angles 3 and 6 are co-interior, so they are supplementary.

55° + \angle 6 = 180°

\angle 6 = 180° - 55° = 125°

⟹ 125°

Compare this with the alternate interior angle, which would have been 55° — equal rather than supplementary. Reading the position correctly is what decides which rule to use.

Example The perpendicular case

What happens when the transversal is perpendicular to the two parallel lines?

Every interior angle becomes a right angle, so each measures 90°.

90° + 90° = 180°

⟹ the rule still holds, with both angles equal

This special case is a useful check on the general rule: it is the one situation where co-interior angles are equal and supplementary at the same time, because 90° is exactly half of 180°.

Note Telling the pairs apart

Co-interior — interior, same side of the transversal → add to 180°.

Alternate interior — interior, opposite sides → equal.

Corresponding — same position at each crossing → equal.

One question separates the first two: are the angles on the same side of the transversal or on opposite sides?

Note Mistakes to avoid

Assuming co-interior angles are equal — they are supplementary instead.

Using the rule when the lines are not parallel.

Picking angles on opposite sides, which makes them alternate interior.

Including an exterior angle; both must lie between the two lines.

Subtracting from 90° rather than 180°.

Summary

Co-interior angles lie between two lines, on the same side of the transversal.
When the lines are parallel they add to 180°: angle 3 + angle 6 and angle 4 + angle 5.
As one angle grows the other shrinks by the same amount, keeping the total fixed.
A perpendicular transversal makes every interior angle 90°, and 90 + 90 = 180 still works.
Same side means supplementary; opposite sides means equal.