Angle facts are the fundamental rules about angles that underpin all geometric reasoning. You must know them and be able to state them as reasons in proofs.
Key angle facts:
- Angles on a straight line sum to $180°$
- Angles around a point sum to $360°$
- Vertically opposite angles are equal
- Angles in a triangle sum to $180°$
- Angles in a quadrilateral sum to $360°$
Parallel lines:
- Alternate angles ("Z angles") are equal
- Corresponding angles ("F angles") are equal
- Co-interior angles ("C angles") sum to $180°$
Example: Find the missing angle in a triangle with angles $47°$ and $83°$: $$180° - 47° - 83° = 50°$$
Always give a reason in geometric proofs — write e.g. "angles in a triangle sum to 180°" rather than just the calculation.
Common error: confusing alternate angles (Z) with corresponding angles (F), or forgetting that co-interior angles add up to 180° (not equal).