Year 6 Mathematics · AC9M6M04

Angle Relationships on Lines and at Points

Use straight, full-turn and vertically opposite relationships to find unknowns

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Learning goalsSay it simply

Learning goal

Students use 180° on a straight line, 360° at a point and equality of vertically opposite angles, combining relationships without relying only on visual appearance.

Success criteria

  • I can represent or identify the concept.
  • I can explain the underlying relationship.
  • I can select an appropriate strategy or feature.
  • I can apply it in a new context.
  • I can justify and verify the response.

Teaching routine

  1. Represent
  2. Reason
  3. Calculate
  4. Interpret
  5. Verify
Curriculum focus: identify and use the relationships between angles on a straight line, angles at a point and vertically opposite angles to solve problems
Key conceptTeach from the board

Connect three fundamental angle relationships

Use the visual model first. Ask students to identify the quantities, structure or conditions before calculating or explaining.

relationshipequationstraight linea + b = 180°angles at a pointa + b + c + … = 360°vertically oppositea = c and b = dright angleparts total 90°

The diagram may not be drawn to scale. Mark the relevant relationship and write an equation before calculating.

Solve linked unknown-angle problems

Connect the central relationship to a new context, then verify the conclusion with a second representation, estimate, inverse operation or reasonableness check.

55°55°
125° supplement125°
right90°
reflex at point235°

A single problem may require vertically opposite equality followed by a straight-line sum or a full-turn total.

Clean visual examplesOne-page board

Clean one-page examples

AC9M6M04 - Angle Relationships on Lines and at Points
Example 1

relationship equation straight line a + b = 180° angles at a point a + b + c + … = 360° vertically opposite a = c and b = d right angle parts total 90°

Example 2

: using protractors or dynamic geometry software to measure and generalise about the size of angles formed when lines are crossed, and combinations of angles that meet at a point, including combinations that form right or straight angles

Example 3

: demonstrating the meaning of language associated with properties of angles, including right, complementary, complement, straight, supplement, vertically opposite, and angles at a point

Example 4

: using the properties of supplementary and complementary angles to represent spatial situations with number sentences and solving to find the size of unknown angles

Curriculum examplesCopied content

AC9M6M04: identify the relationships between angles on a straight line, angles at a point and vertically opposite angles; use these to determine unknown angles, communicating reasoning

  • E1: using protractors or dynamic geometry software to measure and generalise about the size of angles formed when lines are crossed, and combinations of angles that meet at a point, including combinations that form right or straight angles
  • E2: demonstrating the meaning of language associated with properties of angles, including right, complementary, complement, straight, supplement, vertically opposite, and angles at a point
  • E3: using the properties of supplementary and complementary angles to represent spatial situations with number sentences and solving to find the size of unknown angles

Use the central and application models above to connect each elaboration to the same underlying concept.

Questions and answersWith answers

Check understanding

  • Find a supplement.
  • Use vertical opposites.
  • Sum at a point.
  • Write an equation.
  • Check 360° total.

Evidence of mastery

  • Represent or identify the concept
  • Explain the underlying relationship
  • Select an appropriate strategy or feature
  • Apply it in a new context
  • Justify and verify the response

Decision: continue when students can explain the model, apply it to a new example and justify their check. Otherwise return to the central model and reduce the numerical or representational load.

Practice and reviewReady for practice
Diagram measured instead of relationship usedUse given values and geometric facts.
Adjacent and vertically opposite confusedOpposite angles do not share a side.
180° used around a pointA full turn totals 360°.
Reflex angle omittedInclude the stated turn region.
Curriculum alignmentStart here

Learning goal

Students use 180° on a straight line, 360° at a point and equality of vertically opposite angles, combining relationships without relying only on visual appearance.

Success criteria

  • I can represent or identify the concept.
  • I can explain the underlying relationship.
  • I can select an appropriate strategy or feature.
  • I can apply it in a new context.
  • I can justify and verify the response.

Teaching routine

  1. Represent
  2. Reason
  3. Calculate
  4. Interpret
  5. Verify
Curriculum focus: identify and use the relationships between angles on a straight line, angles at a point and vertically opposite angles to solve problems
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