Angles in triangles (age 10+)

PROCEDURAL

Mathematics›Geometry|Ages 10—11|ID: mt_cdMlC7EpTJ

Find unknown angles in triangles, quadrilaterals, and regular polygons using angle sum properties

Mastery Evidence

Find a missing angle in a triangle given two angles (using angle sum = 180°)
Calculate a missing angle in a quadrilateral (angle sum = 360°)
Calculate the interior angle of a regular hexagon from the angle sum formula

Assessment Prompt

“If [child] knows that angles in a triangle always add up to 180°, and two angles in a triangle are 55° and 70°, can they work out the third angle without measuring it?”

Prerequisites3

Types of angles (age 8+)
hardAges 8—12
Classifying shapes by properties
hardAges 10—11
Angle Sum Rules
hardAges 9—10

Show full prerequisite tree

Types of angles (age 8+) hard
Finding unknown angles in polygons requires reading diagrams where known angles are marked with arcs and tick marks
Classifying shapes by properties hard
Finding angles in polygons requires knowing shape properties
- Regular and irregular polygons hard
  Hierarchy includes regular/irregular distinction from Y5
  - Understanding angles (age 8+) hard
    Shape classification supports distinguishing regular from irregular
    - 2-D shapes (age 6+) hard
      Identifying 2D shape properties is prerequisite to classifying by shared attributes
      - Angles in triangles (age 6+) soft
        Understanding defining attributes supports describing shape properties formally
        
        2-D shapes hard
        Distinguishing defining vs non-defining attributes requires knowing common 2-D shape names first
        
        3-D shapes (age 5+) hard
        Identifying defining attributes builds on informal analysis and comparison of shapes
        
        2-D shapes hard
        Analysing and comparing shapes requires being able to name them first
        
        3-D shapes hard
        Analysing 3-D shapes requires recognising and naming them
      - 2-D shapes hard
        Describing properties of 2-D shapes (sides, symmetry) requires knowing the shapes first
      - 3-D shapes (age 5+) hard
        Formal property description extends informal analysis of sides and vertices
        
        2-D shapes hard
        Analysing and comparing shapes requires being able to name them first
        
        3-D shapes hard
        Analysing 3-D shapes requires recognising and naming them
    - Angles in triangles (age 7+) hard
      Recognising shapes by attributes is prerequisite to quadrilateral hierarchy classification
      - Angles in triangles (age 6+) hard
        Drawing shapes by attributes extends understanding defining vs non-defining attributes
        
        2-D shapes hard
        Distinguishing defining vs non-defining attributes requires knowing common 2-D shape names first
        
        3-D shapes (age 5+) hard
        Identifying defining attributes builds on informal analysis and comparison of shapes
        
        2-D shapes hard
        Analysing and comparing shapes requires being able to name them first
        
        3-D shapes hard
        Analysing 3-D shapes requires recognising and naming them
      - 2-D shapes (age 6+) hard
        Identifying pentagons, hexagons, quadrilaterals extends knowing 2-D shape properties
        
        Angles in triangles (age 6+) soft
        Understanding defining attributes supports describing shape properties formally
        
        2-D shapes hard
        Distinguishing defining vs non-defining attributes requires knowing common 2-D shape names first
        
        3-D shapes (age 5+) hard
        Identifying defining attributes builds on informal analysis and comparison of shapes
        
        2-D shapes hard
        Analysing and comparing shapes requires being able to name them first
        
        3-D shapes hard
        Analysing 3-D shapes requires recognising and naming them
        
        2-D shapes hard
        Describing properties of 2-D shapes (sides, symmetry) requires knowing the shapes first
        
        3-D shapes (age 5+) hard
        Formal property description extends informal analysis of sides and vertices
        
        2-D shapes hard
        Analysing and comparing shapes requires being able to name them first
        
        3-D shapes hard
        Analysing 3-D shapes requires recognising and naming them
  - Estimating Angles soft
    Classifying regular/irregular polygons benefits from angle estimation skills
    - Degrees and turns hard
      Estimating/comparing angles requires understanding the degree system
      - What Is an Angle? hard
        Degree measurement system requires understanding what an angle is
        
        Types of angles hard
        Angle definition builds on understanding right angles
        
        Right Angles & Turns hard
        Identifying right angles and greater/less than right angle is prerequisite to naming acute/obtuse
        
        Understanding angles hard
        Identifying right angles requires understanding what an angle is
        
        2-D shapes (age 6+) soft
        Understanding angles as shape properties requires knowing basic shape properties
        
        Angles in triangles (age 6+) soft
        Understanding defining attributes supports describing shape properties formally
        
        2-D shapes hard
        Distinguishing defining vs non-defining attributes requires knowing common 2-D shape names first
        
        3-D shapes (age 5+) hard
        Identifying defining attributes builds on informal analysis and comparison of shapes
        
        2-D shapes hard
        Describing properties of 2-D shapes (sides, symmetry) requires knowing the shapes first
        
        3-D shapes (age 5+) hard
        Formal property description extends informal analysis of sides and vertices
        
        2-D shapes hard
        Analysing and comparing shapes requires being able to name them first
        
        3-D shapes hard
        Analysing 3-D shapes requires recognising and naming them
        
        Position, direction, and movement hard
        Recognising angles as turns extends Y2 work on quarter/half/three-quarter turns
        
        Positional Language hard
        Position/direction vocabulary with right angles extends basic positional language
        
        Turns & Directions hard
        Right-angle turns (clockwise/anti-clockwise) build directly on whole/half/quarter turns from Year 1
        
        What Is a Half? soft
        Understanding half and quarter turns benefits from the concept of halves and quarters
        
        Positional Language hard
        Describing movement and turns builds on positional language
        
        Types of angles (age 8+) soft
        Identifying right angles and turns is supported by the convention of marking right angles with a small square
        
        Position, direction, and movement hard
        Right angles as quarter turns extends Y2 turn vocabulary
        
        Positional Language hard
        Position/direction vocabulary with right angles extends basic positional language
        
        Turns & Directions hard
        Right-angle turns (clockwise/anti-clockwise) build directly on whole/half/quarter turns from Year 1
        
        What Is a Half? soft
        Understanding half and quarter turns benefits from the concept of halves and quarters
        
        Division as equal sharing hard
        Finding a half requires equal sharing into 2 groups — a division concept
        
        Positional Language hard
        Describing movement and turns builds on positional language
        
        Right Angles & Turns hard
        Angle definition builds on classifying acute/obtuse angles
        
        Understanding angles hard
        Identifying right angles requires understanding what an angle is
        
        2-D shapes (age 6+) soft
        Understanding angles as shape properties requires knowing basic shape properties
        
        Angles in triangles (age 6+) soft
        Understanding defining attributes supports describing shape properties formally
        
        2-D shapes hard
        Distinguishing defining vs non-defining attributes requires knowing common 2-D shape names first
        
        3-D shapes (age 5+) hard
        Identifying defining attributes builds on informal analysis and comparison of shapes
        
        2-D shapes hard
        Analysing and comparing shapes requires being able to name them first
        
        3-D shapes hard
        Analysing 3-D shapes requires recognising and naming them
        
        2-D shapes hard
        Describing properties of 2-D shapes (sides, symmetry) requires knowing the shapes first
        
        3-D shapes (age 5+) hard
        Formal property description extends informal analysis of sides and vertices
        
        2-D shapes hard
        Analysing and comparing shapes requires being able to name them first
        
        3-D shapes hard
        Analysing 3-D shapes requires recognising and naming them
        
        Position, direction, and movement hard
        Recognising angles as turns extends Y2 work on quarter/half/three-quarter turns
        
        Positional Language hard
        Position/direction vocabulary with right angles extends basic positional language
        
        Turns & Directions hard
        Right-angle turns (clockwise/anti-clockwise) build directly on whole/half/quarter turns from Year 1
        
        What Is a Half? soft
        Understanding half and quarter turns benefits from the concept of halves and quarters
        
        Division as equal sharing hard
        Finding a half requires equal sharing into 2 groups — a division concept
        
        Positional Language hard
        Describing movement and turns builds on positional language
        
        Types of angles (age 8+) soft
        Identifying right angles and turns is supported by the convention of marking right angles with a small square
        
        Position, direction, and movement hard
        Right angles as quarter turns extends Y2 turn vocabulary
        
        Positional Language hard
        Position/direction vocabulary with right angles extends basic positional language
        
        Turns & Directions hard
        Right-angle turns (clockwise/anti-clockwise) build directly on whole/half/quarter turns from Year 1
        
        What Is a Half? soft
        Understanding half and quarter turns benefits from the concept of halves and quarters
        
        Division as equal sharing hard
        Finding a half requires equal sharing into 2 groups — a division concept
        
        Subtraction as taking away or separating hard
        Division as equal sharing/grouping requires understanding subtraction as taking away/separating
        
        Positional Language hard
        Describing movement and turns builds on positional language
- Classifying shapes by line properties hard
  Property-based hierarchy extends Y5 classification by parallel/perpendicular lines
  - Lines, Rays & Angles hard
    Must draw/identify geometric elements before classifying shapes by them
    - Types of angles hard
      Y4 acute/obtuse angle identification is prerequisite to drawing and labelling angle types
      - Right Angles & Turns hard
        Identifying right angles and greater/less than right angle is prerequisite to naming acute/obtuse
        
        Understanding angles hard
        Identifying right angles requires understanding what an angle is
        
        2-D shapes (age 6+) soft
        Understanding angles as shape properties requires knowing basic shape properties
        
        Angles in triangles (age 6+) soft
        Understanding defining attributes supports describing shape properties formally
        
        2-D shapes hard
        Distinguishing defining vs non-defining attributes requires knowing common 2-D shape names first
        
        3-D shapes (age 5+) hard
        Identifying defining attributes builds on informal analysis and comparison of shapes
        
        2-D shapes hard
        Analysing and comparing shapes requires being able to name them first
        
        3-D shapes hard
        Analysing 3-D shapes requires recognising and naming them
        
        2-D shapes hard
        Describing properties of 2-D shapes (sides, symmetry) requires knowing the shapes first
        
        3-D shapes (age 5+) hard
        Formal property description extends informal analysis of sides and vertices
        
        2-D shapes hard
        Analysing and comparing shapes requires being able to name them first
        
        3-D shapes hard
        Analysing 3-D shapes requires recognising and naming them
        
        Position, direction, and movement hard
        Recognising angles as turns extends Y2 work on quarter/half/three-quarter turns
        
        Positional Language hard
        Position/direction vocabulary with right angles extends basic positional language
        
        Turns & Directions hard
        Right-angle turns (clockwise/anti-clockwise) build directly on whole/half/quarter turns from Year 1
        
        What Is a Half? soft
        Understanding half and quarter turns benefits from the concept of halves and quarters
        
        Division as equal sharing hard
        Finding a half requires equal sharing into 2 groups — a division concept
        
        Subtraction as taking away or separating hard
        Division as equal sharing/grouping requires understanding subtraction as taking away/separating
        
        Positional Language hard
        Describing movement and turns builds on positional language
        
        Types of angles (age 8+) soft
        Identifying right angles and turns is supported by the convention of marking right angles with a small square
        
        Position, direction, and movement hard
        Right angles as quarter turns extends Y2 turn vocabulary
        
        Positional Language hard
        Position/direction vocabulary with right angles extends basic positional language
        
        Turns & Directions hard
        Right-angle turns (clockwise/anti-clockwise) build directly on whole/half/quarter turns from Year 1
        
        What Is a Half? soft
        Understanding half and quarter turns benefits from the concept of halves and quarters
        
        Division as equal sharing hard
        Finding a half requires equal sharing into 2 groups — a division concept
        
        Subtraction as taking away or separating hard
        Division as equal sharing/grouping requires understanding subtraction as taking away/separating
        
        How Many in Total? hard
        Understanding subtraction as taking away requires knowing numbers represent quantities (cardinality)
        
        Positional Language hard
        Describing movement and turns builds on positional language
    - Parallel and perpendicular lines hard
      Y3 horizontal/vertical/perpendicular/parallel lines is prerequisite to drawing and identifying them formally
      - Right Angles & Turns hard
        Perpendicular lines require understanding right angles
        
        Understanding angles hard
        Identifying right angles requires understanding what an angle is
        
        2-D shapes (age 6+) soft
        Understanding angles as shape properties requires knowing basic shape properties
        
        Angles in triangles (age 6+) soft
        Understanding defining attributes supports describing shape properties formally
        
        2-D shapes hard
        Distinguishing defining vs non-defining attributes requires knowing common 2-D shape names first
        
        3-D shapes (age 5+) hard
        Identifying defining attributes builds on informal analysis and comparison of shapes
        
        2-D shapes hard
        Analysing and comparing shapes requires being able to name them first
        
        3-D shapes hard
        Analysing 3-D shapes requires recognising and naming them
        
        2-D shapes hard
        Describing properties of 2-D shapes (sides, symmetry) requires knowing the shapes first
        
        3-D shapes (age 5+) hard
        Formal property description extends informal analysis of sides and vertices
        
        2-D shapes hard
        Analysing and comparing shapes requires being able to name them first
        
        3-D shapes hard
        Analysing 3-D shapes requires recognising and naming them
        
        Position, direction, and movement hard
        Recognising angles as turns extends Y2 work on quarter/half/three-quarter turns
        
        Positional Language hard
        Position/direction vocabulary with right angles extends basic positional language
        
        Turns & Directions hard
        Right-angle turns (clockwise/anti-clockwise) build directly on whole/half/quarter turns from Year 1
        
        What Is a Half? soft
        Understanding half and quarter turns benefits from the concept of halves and quarters
        
        Division as equal sharing hard
        Finding a half requires equal sharing into 2 groups — a division concept
        
        Subtraction as taking away or separating hard
        Division as equal sharing/grouping requires understanding subtraction as taking away/separating
        
        Positional Language hard
        Describing movement and turns builds on positional language
        
        Types of angles (age 8+) soft
        Identifying right angles and turns is supported by the convention of marking right angles with a small square
        
        Position, direction, and movement hard
        Right angles as quarter turns extends Y2 turn vocabulary
        
        Positional Language hard
        Position/direction vocabulary with right angles extends basic positional language
        
        Turns & Directions hard
        Right-angle turns (clockwise/anti-clockwise) build directly on whole/half/quarter turns from Year 1
        
        What Is a Half? soft
        Understanding half and quarter turns benefits from the concept of halves and quarters
        
        Division as equal sharing hard
        Finding a half requires equal sharing into 2 groups — a division concept
        
        Subtraction as taking away or separating hard
        Division as equal sharing/grouping requires understanding subtraction as taking away/separating
        
        How Many in Total? hard
        Understanding subtraction as taking away requires knowing numbers represent quantities (cardinality)
        
        Positional Language hard
        Describing movement and turns builds on positional language
      - Positional Language soft
        Horizontal/vertical builds on positional vocabulary
  - Understanding angles (age 8+) hard
    Y4 quadrilateral classification supports classifying by lines/angles
    - 2-D shapes (age 6+) hard
      Identifying 2D shape properties is prerequisite to classifying by shared attributes
      - Angles in triangles (age 6+) soft
        Understanding defining attributes supports describing shape properties formally
        
        2-D shapes hard
        Distinguishing defining vs non-defining attributes requires knowing common 2-D shape names first
        
        3-D shapes (age 5+) hard
        Identifying defining attributes builds on informal analysis and comparison of shapes
        
        2-D shapes hard
        Analysing and comparing shapes requires being able to name them first
        
        3-D shapes hard
        Analysing 3-D shapes requires recognising and naming them
      - 2-D shapes hard
        Describing properties of 2-D shapes (sides, symmetry) requires knowing the shapes first
      - 3-D shapes (age 5+) hard
        Formal property description extends informal analysis of sides and vertices
        
        2-D shapes hard
        Analysing and comparing shapes requires being able to name them first
        
        3-D shapes hard
        Analysing 3-D shapes requires recognising and naming them
    - Angles in triangles (age 7+) hard
      Recognising shapes by attributes is prerequisite to quadrilateral hierarchy classification
      - Angles in triangles (age 6+) hard
        Drawing shapes by attributes extends understanding defining vs non-defining attributes
        
        2-D shapes hard
        Distinguishing defining vs non-defining attributes requires knowing common 2-D shape names first
        
        3-D shapes (age 5+) hard
        Identifying defining attributes builds on informal analysis and comparison of shapes
        
        2-D shapes hard
        Analysing and comparing shapes requires being able to name them first
        
        3-D shapes hard
        Analysing 3-D shapes requires recognising and naming them
      - 2-D shapes (age 6+) hard
        Identifying pentagons, hexagons, quadrilaterals extends knowing 2-D shape properties
        
        Angles in triangles (age 6+) soft
        Understanding defining attributes supports describing shape properties formally
        
        2-D shapes hard
        Distinguishing defining vs non-defining attributes requires knowing common 2-D shape names first
        
        3-D shapes (age 5+) hard
        Identifying defining attributes builds on informal analysis and comparison of shapes
        
        2-D shapes hard
        Analysing and comparing shapes requires being able to name them first
        
        3-D shapes hard
        Analysing 3-D shapes requires recognising and naming them
        
        2-D shapes hard
        Describing properties of 2-D shapes (sides, symmetry) requires knowing the shapes first
        
        3-D shapes (age 5+) hard
        Formal property description extends informal analysis of sides and vertices
        
        2-D shapes hard
        Analysing and comparing shapes requires being able to name them first
        
        3-D shapes hard
        Analysing 3-D shapes requires recognising and naming them
Angle Sum Rules hard
Finding unknown angles builds on Y5 angle sum facts (180°, 360°)
- Types of angles (age 8+) hard
  Angle sum rules (360° at a point, 180° on a line) are applied through reading angle diagrams with correct notation
- Degrees and turns hard
  Angle facts (at a point = 360°) require degree system knowledge
  - What Is an Angle? hard
    Degree measurement system requires understanding what an angle is
    - Types of angles hard
      Angle definition builds on understanding right angles
      - Right Angles & Turns hard
        Identifying right angles and greater/less than right angle is prerequisite to naming acute/obtuse
        
        Understanding angles hard
        Identifying right angles requires understanding what an angle is
        
        2-D shapes (age 6+) soft
        Understanding angles as shape properties requires knowing basic shape properties
        
        Angles in triangles (age 6+) soft
        Understanding defining attributes supports describing shape properties formally
        
        2-D shapes hard
        Distinguishing defining vs non-defining attributes requires knowing common 2-D shape names first
        
        3-D shapes (age 5+) hard
        Identifying defining attributes builds on informal analysis and comparison of shapes
        
        2-D shapes hard
        Analysing and comparing shapes requires being able to name them first
        
        3-D shapes hard
        Analysing 3-D shapes requires recognising and naming them
        
        2-D shapes hard
        Describing properties of 2-D shapes (sides, symmetry) requires knowing the shapes first
        
        3-D shapes (age 5+) hard
        Formal property description extends informal analysis of sides and vertices
        
        2-D shapes hard
        Analysing and comparing shapes requires being able to name them first
        
        3-D shapes hard
        Analysing 3-D shapes requires recognising and naming them
        
        Position, direction, and movement hard
        Recognising angles as turns extends Y2 work on quarter/half/three-quarter turns
        
        Positional Language hard
        Position/direction vocabulary with right angles extends basic positional language
        
        Turns & Directions hard
        Right-angle turns (clockwise/anti-clockwise) build directly on whole/half/quarter turns from Year 1
        
        What Is a Half? soft
        Understanding half and quarter turns benefits from the concept of halves and quarters
        
        Division as equal sharing hard
        Finding a half requires equal sharing into 2 groups — a division concept
        
        Subtraction as taking away or separating hard
        Division as equal sharing/grouping requires understanding subtraction as taking away/separating
        
        Positional Language hard
        Describing movement and turns builds on positional language
        
        Types of angles (age 8+) soft
        Identifying right angles and turns is supported by the convention of marking right angles with a small square
        
        Position, direction, and movement hard
        Right angles as quarter turns extends Y2 turn vocabulary
        
        Positional Language hard
        Position/direction vocabulary with right angles extends basic positional language
        
        Turns & Directions hard
        Right-angle turns (clockwise/anti-clockwise) build directly on whole/half/quarter turns from Year 1
        
        What Is a Half? soft
        Understanding half and quarter turns benefits from the concept of halves and quarters
        
        Division as equal sharing hard
        Finding a half requires equal sharing into 2 groups — a division concept
        
        Subtraction as taking away or separating hard
        Division as equal sharing/grouping requires understanding subtraction as taking away/separating
        
        How Many in Total? hard
        Understanding subtraction as taking away requires knowing numbers represent quantities (cardinality)
        
        Positional Language hard
        Describing movement and turns builds on positional language
    - Right Angles & Turns hard
      Angle definition builds on classifying acute/obtuse angles
      - Understanding angles hard
        Identifying right angles requires understanding what an angle is
        
        2-D shapes (age 6+) soft
        Understanding angles as shape properties requires knowing basic shape properties
        
        Angles in triangles (age 6+) soft
        Understanding defining attributes supports describing shape properties formally
        
        2-D shapes hard
        Distinguishing defining vs non-defining attributes requires knowing common 2-D shape names first
        
        3-D shapes (age 5+) hard
        Identifying defining attributes builds on informal analysis and comparison of shapes
        
        2-D shapes hard
        Analysing and comparing shapes requires being able to name them first
        
        3-D shapes hard
        Analysing 3-D shapes requires recognising and naming them
        
        2-D shapes hard
        Describing properties of 2-D shapes (sides, symmetry) requires knowing the shapes first
        
        3-D shapes (age 5+) hard
        Formal property description extends informal analysis of sides and vertices
        
        2-D shapes hard
        Analysing and comparing shapes requires being able to name them first
        
        3-D shapes hard
        Analysing 3-D shapes requires recognising and naming them
        
        Position, direction, and movement hard
        Recognising angles as turns extends Y2 work on quarter/half/three-quarter turns
        
        Positional Language hard
        Position/direction vocabulary with right angles extends basic positional language
        
        Turns & Directions hard
        Right-angle turns (clockwise/anti-clockwise) build directly on whole/half/quarter turns from Year 1
        
        What Is a Half? soft
        Understanding half and quarter turns benefits from the concept of halves and quarters
        
        Division as equal sharing hard
        Finding a half requires equal sharing into 2 groups — a division concept
        
        Subtraction as taking away or separating hard
        Division as equal sharing/grouping requires understanding subtraction as taking away/separating
        
        How Many in Total? hard
        Understanding subtraction as taking away requires knowing numbers represent quantities (cardinality)
        
        Positional Language hard
        Describing movement and turns builds on positional language
      - Types of angles (age 8+) soft
        Identifying right angles and turns is supported by the convention of marking right angles with a small square
      - Position, direction, and movement hard
        Right angles as quarter turns extends Y2 turn vocabulary
        
        Positional Language hard
        Position/direction vocabulary with right angles extends basic positional language
        
        Turns & Directions hard
        Right-angle turns (clockwise/anti-clockwise) build directly on whole/half/quarter turns from Year 1
        
        What Is a Half? soft
        Understanding half and quarter turns benefits from the concept of halves and quarters
        
        Division as equal sharing hard
        Finding a half requires equal sharing into 2 groups — a division concept
        
        Subtraction as taking away or separating hard
        Division as equal sharing/grouping requires understanding subtraction as taking away/separating
        
        How Many in Total? hard
        Understanding subtraction as taking away requires knowing numbers represent quantities (cardinality)
        
        One-to-one counting hard
        Cardinality principle builds on one-to-one correspondence — you must count correctly to know the last number tells 'how many'
        
        Positional Language hard
        Describing movement and turns builds on positional language

Unlocks3

Generalising with repeated reasoning
softAges 10—11
Angle sums in triangles and polygons
hardAges 11—14
Constructing mathematical arguments
softAges 10—11