Angles, Polygons & Parallel Lines — Year 8 Revision Notes
These notes cover basic angle facts, the angles formed by parallel lines, and the interior and exterior angles of polygons — all at Year 8 (Stage 8) level, with reasons for each step.
Basic angle facts
Angles on a straight line add to 180°, angles around a point add to 360°, and the angles in a triangle add to 180°. Vertically opposite angles, formed when two lines cross, are equal. These facts are the building blocks for every angle calculation.
Key Facts & Formulas
- Straight line = 180°
- Around a point = 360°
- Triangle = 180°
Tips
- State which fact you used as your reason.
- Look for triangles and straight lines hidden in the diagram.
Angles in parallel lines
When a transversal crosses two parallel lines: corresponding angles (F-shape) are equal, alternate angles (Z-shape) are equal, and co-interior angles (C-shape) add to 180°. Use these to find unknown angles, and always name the rule you used.
Key Facts & Formulas
- Corresponding angles equal
- Alternate angles equal
- Co-interior angles = 180°
Tips
- Spot the F, Z and C shapes in the diagram.
- Co-interior angles add to 180°, they are not equal.
Angles in polygons
The interior angles of a polygon with n sides add up to 180 × (n − 2). For a regular polygon every interior angle is equal, so divide that sum by n. The exterior angles of any polygon always add up to 360°, so each exterior angle of a regular polygon is 360 ÷ n.
Key Facts & Formulas
- Interior angle sum = 180 × (n − 2)
- Exterior angle (regular) = 360 ÷ n
- Interior + exterior = 180°
Tips
- Exterior angles always total 360°, whatever the polygon.
- Interior + exterior angle at a vertex = 180°.
Revision Checklist
- I can use basic angle facts and give reasons
- I can find angles in parallel lines using corresponding, alternate and co-interior angles
- I can find the interior angle sum of any polygon
- I can find interior and exterior angles of a regular polygon
Frequently Asked Questions
Do exterior angles always add up to 360°?
Yes — for any convex polygon, no matter how many sides, the exterior angles always sum to 360°. That is why each exterior angle of a regular polygon is 360 ÷ n.
Build strong foundations in Angles, Polygons & Parallel Lines
A free trial class with Teacher Rig helps your Year 8 child master Angles, Polygons & Parallel Lines now — so IGCSE Maths feels familiar, not frightening, later.
Heading toward IGCSE? See how Angles, Polygons & Parallel Lines develops in IGCSE Geometry (Cambridge 0580) →