Skip to main content
    Achieve Academy
    Back to Resources

    Geometry & Measures

    Revision notes · Maths

    Formula SheetPractice bookletsFlashcards
    Tier
    Practise questions
    Lesson step 1 of 4Angles & Polygons

    Angles & Polygons

    Angle facts are the foundation of geometry questions. Make sure you know these rules and can state them clearly — examiners want to see reasons, not just numbers.

    Basic angle facts:

    Angles in a triangle add up to 180°

    Angles in a quadrilateral add up to 360°

    Angles on a straight line add up to 180°

    Angles around a point add up to 360°

    Vertically opposite angles are equal

    With parallel lines, there are three key angle relationships:

    Alternate angles are equal (Z-shape)

    Corresponding angles are equal (F-shape)

    Co-interior (allied) angles add up to 180° (C-shape or U-shape)

    Always look for the letter shape to identify which rule applies. Draw the Z, F, or C onto the diagram if it helps.

    For regular polygons, you need to know the key formulas for interior and exterior angles — see the reference poster below for all the formulas, a worked example, and a handy lookup table.

    1 / 11

    Key Terms

    Pythagoras' theorem
    a² + b² = c² — a rule that works in right-angled triangles. The two shorter sides squared and added together equal the longest side squared.
    Similar shapes
    Shapes that look the same but are different sizes — all the angles match and the sides are in the same ratio.
    Congruent shapes
    Shapes that are exactly the same — same shape AND same size. Like identical copies.
    Sector
    A 'pizza slice' shape from a circle — the region between two straight lines from the centre (radii) and the curved edge (arc).