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GCSE Mathematics 04 — Geometry and Measures

Public

Topics include Angles and Parallel Lines, Polygons, Triangles and Congruence, Quadrilaterals, 2D Area and Perimeter, Circle Theorems, Arcs and Sectors, and Pythagoras and SOHCAHTOA.

Mathematics EN
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Angles and Parallel Lines

Fundamental angle rules relating to straight lines, points, triangles, and parallel lines intersected by transversals.

Key points

  • Angles on a straight line sum to 180∘180^\circ.
  • Angles at a point sum to 360∘360^\circ.
  • Vertically opposite angles are equal.
  • Alternate angles (Z-angles) on parallel lines are equal.
  • Corresponding angles (F-angles) on parallel lines are equal.

Worked example

Question

Two parallel lines are intersected by a transversal. One of the interior angles is 115∘115^\circ. Calculate the size of the consecutive interior (co-interior) angle and justify your answer.

Solution

1. Identify the relationship: The angles are co-interior (allied).
2. Apply the rule: Co-interior angles sum to 180∘180^\circ.
3. Calculation: 180∘−115∘=65∘180^\circ - 115^\circ = 65^\circ.
4. Justification: Co-interior angles between parallel lines sum to 180∘180^\circ.

Common pitfalls

  • Confusing alternate (Z) and corresponding (F) angles.
  • Assuming alternate/corresponding angles are equal when lines are not marked as parallel.
  • Thinking co-interior angles are equal (they sum to 180).
  • Forgetting to subtract from 180 or 360 in basic angle problems.

Prerequisites

  • Basic arithmetic
  • Definition of parallel lines
Further resources