Angles in Parallel Lines and Polygons

Scheme of work: Key Stage 3: Year 8: Term 1: Angles in Parallel Lines and Polygons

Prerequisite Knowledge

  • Draw and measure line segments and angles in geometric figures, including interpreting scale drawings.
  • Apply the properties of angles at a point, angles at a point on a straight line, vertically opposite angles
  • Derive and use the sum of angles in a triangle and use it to deduce the angle sum in any polygon

Key Concepts

  • Alternate angles appear in ordinary and stretched-out Z shapes and are equal.
  • Corresponding angles appear in F shapes.  The F shape can be reflected or rotated.  Corresponding angles are equal.
  • Interior angles appear in C shapes and have a sum of 180°.
  • Students should be able to prove each angle property using algebraic notation.
  • Students need to be able to combine multiple angle properties to solve a larger problem.
  • All the exterior angles of a polygon have a sum of 360°.
  • An interior and exterior angle lie along a straight line.  Therefore interior plus exterior angle equals 180°.
  • Students are often expected to combine multiple angle properties when calculating angles in polygons.

Working Mathematically

  • Develop fluency
    • Use language and properties precisely to analyse 2-D shapes
    • Select and use appropriate calculation strategies to solve increasingly complex problems
    • Reason mathematically
    • Make and test conjectures about patterns and relationships; look for proofs or counter-examples
    • Begin to reason deductively in geometry, including using geometrical constructions
  • Solve problems
    • Develop their mathematical knowledge, in part through solving problems and evaluating the outcomes, including multi-step problems.

Subject Content

  • Shape
    • Understand and use the relationship between parallel lines and alternate and corresponding angles.
    • Derive and use the sum of angles in a triangle and use it to deduce the angle sum in any polygon, and to derive properties of regular polygons

Angles in Parallel Lines and Polygons Resources

Mr Mathematics Blog

Problem-Solving with Angles in Polygons

How to teach problem solving with angles in polygons through scaffolding.

The Sum to Infinity of Geometric Series – A-Level Maths Tutorial

Explore geometric series in our A-Level Maths tutorial. Perfect for students/teachers, with resources to download at

Sequences and Series

Edexcel A-Level Mathematics Year 2: Pure 2: Algebraic Methods