O-Level E-Math and SEC G3 Mathematics K310
G1: Angles, triangles and polygons
Use angle facts and polygon properties with reasons stated rather than relying on diagram appearance.
Core notes
Geometry arguments depend on named facts, not visual appearance. Mark the diagram, state the angle or shape property used, and keep construction arcs visible when a construction is required.
Basic angle facts
Angles may be acute, right, obtuse or reflex. Vertically opposite angles are equal, angles on a straight line sum to , and angles at a point sum to .
Parallel lines and transversals
For parallel lines, corresponding and alternate angles are equal, while co-interior angles sum to . The parallel condition must be known or proved before these facts are used.
Triangles, quadrilaterals and polygons
Use side, angle, parallelism and symmetry properties to classify a shape. A regular polygon has equal sides and equal interior angles. The interior-angle sum of a convex -gon is , while its exterior angles sum to .
Geometrical constructions
Construct lengths and angles from the given data with compasses, ruler, set squares or protractor as appropriate. Construction arcs are evidence of the method and should not be erased.
Formulae and methods
| Relationship | Use |
|---|---|
| Find the total interior angle of a convex polygon. | |
| Find one exterior angle of a regular polygon. |
Worked examples
Example 1: Find one interior angle of a regular decagon.
- A decagon has .
- Its exterior angle is .
- The interior angle is .
Answer: Each interior angle is .
Example 2: Two parallel lines are cut by a transversal. An acute angle is . Find the adjacent obtuse angle.
- Adjacent angles on a straight line sum to .
- Calculate .
- State the straight-line reason.
Answer: The obtuse angle is .
Chapter checkpoint
- Identify parallel lines, equal sides and angle markings before calculating.
- State a reason for every angle or classification step.
- For a construction, use the required instruments and retain the arcs.
Exam traps and retrieval check
Avoid these traps
- Using parallel-line facts when parallelism is not given.
- Classifying a quadrilateral from one property that is not sufficient.
- Erasing construction arcs and leaving no evidence of the required method.
Check from memory
What do exterior angles of any convex polygon sum to?
.
What are co-interior angles between parallel lines?
They are supplementary and sum to .
Why must reasons be stated in an angle proof?
They establish that each deduction follows from a valid geometrical property.
Official K310 coverage
This chapter maps to 7 official outcomes: G1.1, G1.2, G1.3, G1.4, G1.5, G1.6, G1.7. Check the official 2027 K310 syllabus for exact assessable wording and paper details.