Angle Facts
Fundamental Angle Rules
| Rule | Fact |
|---|---|
| Angles on a straight line | Sum $= 180°$ |
| Angles around a point | Sum $= 360°$ |
| Vertically opposite angles | Equal |
| Angles in a triangle | Sum $= 180°$ |
| Angles in a quadrilateral | Sum $= 360°$ |
Angles in Parallel Lines
When a transversal crosses two parallel lines, three types of angle pairs are formed:
Corresponding angles (F-shape): Equal
They are in the same position at each intersection.
Alternate angles (Z-shape): Equal
They are on opposite sides of the transversal, between the parallel lines.
Co-interior (same-side interior) angles (C-shape): Sum to 180°
They are on the same side of the transversal, between the parallel lines.
Memory aids:
- Forward for corresponding (F-shape)
- Z for alternate (Z-shape, sometimes called Z angles)
- C for co-interior (C-shape, supplementary)
Angles in Polygons
Interior angles (inside the polygon):
$$\text{Sum of interior angles} = (n - 2) \times 180°$$
where $n$ = number of sides.
| Polygon | Sides | Sum of interior angles | Each interior angle (regular) |
|---|---|---|---|
| Triangle | 3 | 180° | 60° |
| Quadrilateral | 4 | 360° | 90° |
| Pentagon | 5 | 540° | 108° |
| Hexagon | 6 | 720° | 120° |
| Octagon | 8 | 1080° | 135° |
Exterior angles (one at each vertex, formed by extending a side):
$$\text{Sum of exterior angles of any polygon} = 360°$$
For a regular polygon: each exterior angle $= \dfrac{360°}{n}$.
Key link: interior angle $+$ exterior angle $= 180°$ (angles on a straight line).
✦Worked example
Find the number of sides of a regular polygon with interior angle 156°.
Exterior angle $= 180° - 156° = 24°$
Number of sides $= 360° \div 24° = 15$
WJEC Exam Tips
- On WJEC papers, always give a reason for each step (e.g. "alternate angles, $AB \parallel CD$").
- Multi-step angle problems: label the unknown, write an equation, solve.
- Isosceles triangles appear frequently — the two base angles are equal.
- Show the calculation for the interior angle sum even if you know the answer.
AI-generated · claude-opus-4-7 · v3-wjec-maths