Angle facts: parallel lines and polygons
Angle questions appear on every OCR J560 paper. Many marks are given for clear reasoning — state the rule used, not just the answer. OCR mark schemes require justification ("alternate angles are equal" earns marks; "Z-angles" by itself does not in formal responses).
Basic angle facts
| Fact | Rule |
|---|---|
| Angles on a straight line | Sum = 180° |
| Angles at a point | Sum = 360° |
| Vertically opposite angles | Equal |
| Angles in a triangle | Sum = 180° |
| Angles in a quadrilateral | Sum = 360° |
Parallel line angle pairs
When a transversal crosses two parallel lines, three pairs of angles arise:
Alternate angles (Z-angles): equal. Between the parallel lines, on opposite sides of the transversal.
Corresponding angles (F-angles): equal. On the same side of the transversal, one between the parallels and one outside.
Co-interior angles (C-angles / allied angles): supplementary (add to 180°). Between the parallel lines, on the same side of the transversal.
Interior angles of polygons
Sum of interior angles of an n-sided polygon = (n − 2) × 180°
| Shape | n | Interior angle sum |
|---|---|---|
| Triangle | 3 | 180° |
| Quadrilateral | 4 | 360° |
| Pentagon | 5 | 540° |
| Hexagon | 6 | 720° |
| Octagon | 8 | 1080° |
Interior angle of a regular polygon = sum ÷ n.
Example: Regular hexagon interior angle = 720° ÷ 6 = 120°.
Exterior angles of polygons
Sum of ALL exterior angles of ANY polygon = 360°.
Exterior angle of a regular polygon = 360° ÷ n.
Example: Regular pentagon exterior angle = 360° ÷ 5 = 72°.
Interior angle + exterior angle = 180° (angles on a straight line).
Proof questions
OCR J560 asks for geometric proofs requiring full reasoning chains. Each step must reference a named angle fact.
Example proof: "Angles x and y are alternate angles between parallel lines AB and CD, cut by transversal EF. Therefore x = y."
Common OCR exam mistakes
- Confusing alternate and co-interior angles (both look like Z or C shapes but behave differently).
- Forgetting that co-interior angles SUM to 180° (not equal).
- Using "Z-angles" without naming the property — OCR requires "alternate angles are equal."
- Applying the interior angle sum formula incorrectly: using n × 180° instead of (n−2) × 180°.
- Finding exterior angles: dividing by n gives the EXTERIOR angle for a REGULAR polygon only.
AI-generated · claude-opus-4-7 · v3-ocr-maths