3.4 Angle facts
Use line, polygon and circle angle relationships and construct logically ordered geometric proofs.
How to study WJEC GCSE Mathematics and Numeracy
Move from concept and notation to a justified method, show a complete mathematical chain, check scale and units, and interpret the answer in context.
Core concepts
Concept 1
Apply angle facts for lines, triangles, quadrilaterals and parallel lines.
Exam cue: Confirm the unit, entered tier, calculator condition and available formula list before choosing a method.
Concept 2
Use interior and exterior angle relationships in polygons.
Exam cue: Name the angle fact at each step and connect the chain of deductions to the required result.
Concept 3
Apply circle theorems and construct angle-based geometric proofs at the specified tier.
Exam cue: Show a complete mathematical chain, use correct notation and units, and interpret or check the result in its original context.
Concept 4
Current matrix coverage: Unit 1, Unit 2, Unit 3. Read the exact subpoint scope in each applicable unit column.
Concept 5
Foundation content is shown in standard type in the specification; bold additions apply only to Higher Tier.
Risk pitfalls and guardrails
Quoting a circle theorem or parallel-line rule without identifying the relevant points, lines or equal angles.
Guardrail: Do not import the outgoing separate qualifications, assume a universal tier across units or ignore calculator, formula-list, context and accuracy conditions.
Assuming that every subpoint in a cross-unit strand appears in all three papers, rather than reading the correct matrix column.
Guardrail: Read the precise subpoint in the applicable unit column; a cross-unit strand does not mean every subpoint appears in every paper.
Using a Higher-only method or expectation for a Foundation entry, or importing the outgoing Mathematics/Mathematics-Numeracy structure.
Guardrail: Standard type applies to Foundation and Higher; bold specification additions are Higher-only. There is no Intermediate Tier.
Memory anchors
Vertically opposite
Vertically opposite angles are equal.
Alternate angles
Alternate angles between parallel lines are equal.
Co-interior angles
Co-interior angles between parallel lines sum to 180 degrees.
Polygon exterior sum
One exterior angle at each vertex of a polygon sums to 360 degrees.
Circle theorem
A circle theorem is a proved relationship among angles, chords, tangents and radii.
Checkpoint rule
Do the check-up only after you can summarize each concept in one sentence and identify one dangerous pitfall from memory.
Knowledge Check (after reading)
Short check-up to confirm understanding of this module.
Check-up Questions
An angle x° and 67° form a straight line. Find x.
Four rays partition a full turn into 95°, 120°, 68° and one missing sector. Find the missing sector.
Answer all questions to submit.
Next step personalized recommendations
Continue learning
Move forward only after this module is stable.
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