Lines and angles on the ACT center on parallel lines cut by a transversal—corresponding, alternate interior, and alternate exterior angles are equal, while same-side interior angles are supplementary—plus vertical angles and linear pairs around any intersection. Most questions give you one or two angle measures and ask for another; label the diagram and the relationships do the work.
Parallel lines and a transversal
When two parallel lines are crossed by a third line, eight angles form. Equal-angle pairs:
- Corresponding angles—same position at each intersection (e.g., top-left with top-left)
- Alternate interior angles—between the parallels, on opposite sides of the transversal
- Alternate exterior angles—outside the parallels, on opposite sides
Same-side interior angles (consecutive interior) add to 180°. If one is 70°, the other is 110°.
Vertical angles and linear pairs
When any two lines cross, vertical angles are equal and adjacent angles on a straight line sum to 180°. These rules apply even when the lines are not marked parallel—they show up in polygons and multi-line diagrams throughout the section.
Using algebra on angle problems
The ACT often labels angles with expressions like 2x + 10 and 3x − 5. Set equal angles equal, or set supplementary angles to sum to 180°, then solve for x and plug back in for the measure asked. Check that your answer is reasonable (positive, less than 180° for a single angle in a simple diagram).
Perpendicular lines
Perpendicular lines meet at 90°. Right angles appear in triangle height problems, rectangle corners, and coordinate geometry (slopes that are negative reciprocals). See coordinate geometry on the ACT when the setup uses a grid instead of a bare diagram.
Connection to triangles and polygons
Parallel-line rules explain why alternate interior angles in a triangle proof match, and why regular polygons have predictable angle measures. Follow-ups: triangle problems, polygons on ACT Math, and the geometry overview in how much geometry is on the ACT.
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This article offers general ACT prep guidance. The ACT can change from year to year, including its format, scoring, policies, test dates, and fees, so always confirm the latest details on the official ACT website at act.org before you make decisions. ACT® is a registered trademark of ACT, Inc. thirty-six is not affiliated with, endorsed by, or sponsored by ACT.