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PROOF OF INTERIOR AND EXTERIOR ANGLES OF A POLYGON | GEOMETRY MADE EASY
In this video, we dive deep into the proof of interior and exterior angles of a polygon, explaining why the formulas work — not just how to use them. This is an essential concept in Euclidean Geometry and a key topic for SSCE, WAEC, NECO, UTME, IGCSE, and JAMB mathematics students.
We’ll start by revising what a polygon is — a closed plane figure with straight sides — and then move into the mathematical derivation (proof) of:
✅ The sum of interior angles of a polygon = (n – 2) × 180°
✅ The sum of exterior angles of any polygon = 360°
✅ The relationship between each interior and exterior angle in a regular polygon
Through detailed explanations, diagrams, and step-by-step reasoning, you’ll understand how these formulas are derived from basic geometric principles — particularly by dividing a polygon into triangles and using the angle sum property of triangles.

🧮 What You’ll Learn
Meaning and properties of polygons
Derivation of the interior angle formula
Proof that sum of exterior angles = 360°
Relationship between interior and exterior angles
Solved examples to reinforce understanding
Common exam-style questions and tips

🎯 Why Watch This Video?
This lesson doesn’t just tell you to memorize formulas — it helps you understand the logic behind them. Once you grasp this proof, solving any polygon-related question becomes easier and faster in exams.
Whether you’re preparing for WAEC, NECO, UTME, SSCE, IGCSE, or BECE, this video will strengthen your geometry foundation and improve your problem-solving skills.

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