Build and annotate the model
Represent angle relationships on lines and at points and label the important parts, quantities or choices.
Learning goals
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
- Represent
- Reason
- Calculate
- Interpret
- 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 concept
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.
Worked examples
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.
Curriculum elaborations explicitly taught
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.
Common misconceptions
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.
Classroom activities
Compare and reason
Use the application model to compare two cases, explain the relationship and identify a likely error.
Transfer and verify
Apply the idea in an unfamiliar context and use a second method, evidence source or text feature to check it.
Revision Notes and quick mastery check
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.
Curriculum wording and references
Australian Curriculum v9.0
AC9M6M04: identify and use the relationships between angles on a straight line, angles at a point and vertically opposite angles to solve problems
The Australian Curriculum code and wording are exact. International teachers can use the underlying mathematical concept while matching the lesson to their local grade or year outcomes.
Resources and next steps
Teacher Slides
Project the fixed, branded four-page teaching sequence.
Open Classroom ViewHomework
Use the printable activity for written practice.
Open HomeworkPractice and Test
Use supported Practice first, then the separate Test when ready.
Open PracticeOpen Test
🎥 Optional Video Lesson
The SkillrHub lesson remains the primary learning resource. This optional video reinforces the explanation; you can complete the lesson and practice without watching.
Before you watch:
- Pause after each worked example.
- Try the examples yourself.
- Return to the SkillrHub lesson before continuing.
Recommended: Vertical, Adjacent and Linearly Paired Angles
Khan Academy — Use the relationships between opposite angles and angles on a straight line.
As you watch: Why are vertically opposite angles equal when two lines intersect?
Load video player Loads YouTube in this lesson. See the video notice below.
Try it: Two lines cross and one angle is 68°. Find the other three angles and justify each using an angle relationship.
Video unavailable, inaccurate or unsuitable for this year? Report a video problem to SkillrHub by email. You can continue with the written lesson and practice resources.
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Curriculum equivalents: Victoria, NSW and international
Curriculum equivalents for The relationships between angles on a straight line, angles at...
Mapped skill: 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
These references identify matching or closely related learning. Curriculum sequence, terminology and depth vary, so teachers should use the mapped skill and lesson difficulty to confirm suitability.
| Region | Curriculum framework | Closest level or code |
|---|---|---|
| Australia | Australian Curriculum v9.0 | AC9M6M04 · Year 6 |
| Victoria | Victorian Curriculum F–10 Version 2.0 — Mathematics | VC2M6M04 · Level 6 |
| New South Wales | NSW Mathematics K–10 Syllabus (2022) | MA3-GM-03 · Stage 3 |
| United States (USA) | Common Core State Standards for Mathematics | Grade 6 |
| Canada (Ontario) | Ontario Curriculum — Mathematics | Grade 6 |
| United Kingdom (England) | National Curriculum in England — Mathematics | Year 7, Key Stage 3 |
| India | NCERT / CBSE — Mathematics | Class 6 |
Australian Curriculum v9.0 is the canonical source for this SkillrHub lesson. Victoria and NSW entries name the closest published state codes or outcomes; international entries are planning references rather than claims of identical curricula.
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Topic reference: AC9M6M04 — Angle Relationships on Lines and at Points
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