Angle facts

Description

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).

Links

Polygons Circle theorems