Geometry
Co-interior Angles – Same Side, Supplementary
Co-interior angles (also called allied angles) are formed when a transversal crosses two lines: they sit on the same side of the transversal, and between the two lines (interior). Unlike corresponding and alternate angles, co-interior angles are not equal on parallel lines – instead, they are supplementary, summing to exactly 180°.
This is the one relationship in this cluster that follows the “sum to 180” pattern rather than the “equal” pattern, so it's worth double-checking carefully: same side, interior, and supplementary – not equal.
Identifying and Using Co-interior Angles
Co-interior angles lie between two lines, on the same side of the transversal. On parallel lines, co-interior angles are supplementary (sum to 180°), not equal.
Co-interior angles on parallel lines sum to 180°: 180 − 112 = 68°.
Real-Life Application
- Ladder against a wall: the ladder and the wall's edge form co-interior angles with the ground as a parallel reference.
- Awnings and canopies: a sloped awning crossing parallel wall lines creates co-interior angle pairs.
- Escalators: an escalator crossing two parallel floor levels forms co-interior angles at each level.
Key Takeaways
- Co-interior angles lie between two lines, on the same side of the transversal.
- On parallel lines, co-interior angles are supplementary, summing to 180°.
- This is the one relationship in the cluster that is NOT an equal pair.