CORE_MATH • SHS 1Term 3WAEC / WASSCE SyllabusVIP Lesson
Polygons (Interior & Exterior Angles)
Properties of convex polygons, sum of interior angles (2n - 4) × 90°, sum of exterior angles = 360°, regular polygons, and angle calculations.
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Real-World Context & Relevance in Ghana
Kente cloth weavers in Bonwire create intricate geometric patterns utilizing regular hexagonal and octagonal symmetries.
Key Syllabus Learning Objectives
- 1Calculate the sum of interior angles for any n-sided polygon
- 2Determine the number of sides of a regular polygon from its interior or exterior angle
- 3Solve for unknown angles in irregular polygons using angle sum theorems
- 4Apply the exterior angle property (sum = 360°) to simplify complex polygon problems
1
The Exterior Angle Shortcut
When working with regular polygons, finding the exterior angle first is almost always faster than using the interior angle formula. Since each exterior angle is 360°/n and interior + exterior = 180°, one can quickly find n = 360° / (180° - interior angle).
- Exterior angle = 180° - Interior angle.
- Number of sides n = 360° / Exterior angle.
- Avoids dealing with large fractions in (n - 2) × 180°.
Core Takeaway:
Always convert interior angle questions of regular polygons to exterior angles first.
WAEC / WASSCE Examiner Tips
- Always check that your calculated number of sides n is a positive integer greater than or equal to 3. If n is a fraction or negative, check your algebra immediately!
- In irregular polygons, write the sum of all given angles equal to (n - 2) × 180° before collecting terms.
- Remember that an exterior angle is formed by extending ONE side of the polygon.
Common Candidate Pitfalls & Errors to Avoid
- Confusing (n - 2) × 180° with 360° / n.
- Assuming sum of exterior angles depends on n (it is ALWAYS 360° for every convex polygon).
- Forgetting that interior and exterior angles at a vertex are on a straight line and sum to 180°.
Topic Mastery Checklist
- Can I calculate the sum of interior angles of a nonagon (n=9)?
- Can I find the number of sides of a regular polygon whose interior angle is 144°?
- Can I find unknown angles in a pentagon with angles x, 2x, x+30, 2x-10, and 100°?
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