Angles and Lines
Angle questions on the SAT come down to a few rules — straight lines sum to 180°, vertical angles match, and parallel lines cut by a transversal create predictable equal-or-supplementary angle pairs.
| Pair | When | Relationship |
|---|---|---|
| Vertical angles | Two lines cross | EQUAL |
| Linear pair (supplementary) | Two angles on a straight line | Sum = 180° |
| Complementary angles | Two angles together = right angle | Sum = 90° |
| Corresponding angles | Parallel + transversal, same position | EQUAL |
| Alternate interior angles | Parallel + transversal, between, opposite | EQUAL |
| Same-side interior | Parallel + transversal, between, same side | Sum = 180° |
| Polygon | Sides | Angle sum | Each angle (regular) |
|---|---|---|---|
| Triangle | 3 | 180° | 60° |
| Quadrilateral | 4 | 360° | 90° (square) |
| Pentagon | 5 | 540° | 108° |
| Hexagon | 6 | 720° | 120° |
| Octagon | 8 | 1080° | 135° |
Identify which rule applies (straight line, vertical angles, triangle sum, parallel-line rules, polygon sum). Chain rules together if needed to find the unknown angle.
The exterior angle of a triangle measures 130°. One of the non-adjacent interior angles is 70°. What is the other non-adjacent interior angle?
Worked examples
Common pitfalls
Complementary = sum to 90°. Supplementary = sum to 180°. SAT angle problems use both — read carefully.
Just because lines look parallel in a diagram doesn't mean they are. The problem must STATE parallel (or use ∥ symbols). Otherwise don't apply parallel-line angle rules.
If two sides of a triangle are equal, the angles OPPOSITE those sides are also equal. SAT problems often hide this — they tell you a triangle is isosceles and expect you to deduce equal angles.
Key takeaways
Straight line = 180°. Triangle = 180°. Quadrilateral = 360°.
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Vertical angles are equal. Linear pair (on a straight line) sums to 180°.
Parallel + transversal: only TWO distinct angle measures appear.
Exterior angle of a triangle = sum of two non-adjacent interior angles.
Checkpoint
10 questions on Lines, Angles, and Triangles, from our question bank. Score 70% or better across 10 answers to reach Silver and pass this step.