GCSE Maths • Foundation & Higher
GCSE Geometry Revision Guide
Master key angle facts, parallel-line rules and polygon calculations for GCSE Maths.
Foundation
Exam practice
Worked examples
What You'll Learn
Angles on a Line
Use the fact that angles on a straight line add up to 180°.
Angles Around a Point
Use the fact that angles around a point add up to 360°.
Parallel Line Angles
Recognise corresponding, alternate and co-interior angle relationships.
Use Angle Rules with Algebra
Form and solve equations when angles are written as expressions.
Understand Polygons
Recognise common polygons and distinguish between regular and irregular polygons.
Calculate Polygon Angles
Find interior angle sums, regular interior angles, exterior angles and the number of sides.
Key Rules and Formulas
Geometry Lessons
Angles Around a Point
Use the 360° rule to find missing angles, including questions with algebra.
Angles on a Line
Use the 180° straight-line rule to solve numerical and algebraic angle problems.
Polygons
Name polygons and calculate interior-angle sums, regular angles, exterior angles and numbers of sides.
Parallel Line Angles
Identify corresponding, alternate and co-interior angles using F, Z and C patterns.
CORE SUBTOPICS
Straight-Line Angles
Angles on a straight line total 180°. Add the known angles and subtract from 180° to find a missing angle.
Angles Around a Point
Angles meeting at one point total 360°. Add the known angles and subtract from 360°.
Algebraic Angle Problems
Use the relevant angle fact to form an equation, then solve it carefully.
Corresponding, Alternate and Co-Interior Angles
Corresponding and alternate angles are equal, while co-interior angles sum to 180°.
Polygon Names and Types
Common polygons include triangles, quadrilaterals, pentagons, hexagons, heptagons, octagons and decagons.
Interior and Exterior Polygon Angles
Use (n − 2) × 180° for interior-angle sums and remember that exterior angles total 360°.
Worked Example
Using Parallel-Line Angle Rules
QUESTION
Two co-interior angles are x and 120°. Find x.
- Given information: Co-interior angles lie inside parallel lines on the same side of the transversal.
- Method: Co-interior angles add up to 180°.
- Write the angle equation: x + 120 = 180.
- Subtract 120 from both sides.
- x = 60.
- Answer: x = 60°.
- Key idea: Co-interior angles add to 180° when the lines are parallel.
- Common mistake: Do not treat co-interior angles as equal. Corresponding and alternate angles are equal; co-interior angles sum to 180°.
- Common GCSE Mistakes
- Using 360° instead of 180° on a straight line.
- Forgetting one of the angles around a point.
- Mixing up corresponding, alternate and co-interior angles.
- Missing the parallel-line markings.
- Confusing interior and exterior polygon angles.
- Exam Tips
- Write the angle rule before calculating.
- Look for F, Z and C shapes on parallel lines.
- Check whether the total should be 180° or 360°.
- Form an equation carefully when algebra is involved.
- Check polygon formulas and angle totals before finishing.
Ready to Practice?
Printable Worksheet
Practise simplifying, unit conversions, sharing totals, recipe scaling, combined ratios and best-buy comparisons.
Interactive Quiz
Check ratio order, equivalent ratios, total parts, unit prices and common misconceptions.
Exam-Style Questions
Apply ratio methods to money, measures, recipes, maps and multi-stage GCSE contexts.
Watch the Ratio Tutorial Geometry
Clear, step-by-step explanation of expanding brackets, simplifying complex expressions, and solving for x. Perfect for visual learners who need a breakdown of the rules in action.
- 12 minute comprehensive guide
- High-definition whiteboard walk-through
Continue Your GCSE Maths Revision
Continue Your GCSE Maths Revision
Frequently Asked Questions
Angles on a straight line add up to 180°.
Angles around a point add up to 360°.
Corresponding angles are in matching positions when a transversal crosses parallel lines, and they are equal.
Alternate angles lie on opposite sides of a transversal across parallel lines, and they are equal.
