PROOF OF INTERIOR AND EXTERIOR ANGLES OF A POLYGON | GEOMETRY MADE EASY

Описание: 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

This tutorial breaks down every step with clear diagrams, color-coded visuals, and practical explanations — perfect for WAEC, NECO, IGCSE, JAMB, and SSCE students.

🕒 Timestamps & Chapters
00:00:01 - 00:00:42 | Introduction to Polygon Angles and Colors
Learn how to use fill and stroke colors to represent interior and exterior angles in polygons, using a regular pentagon as an example.
00:00:42 - 00:01:20 | Extending Lines for Interior and Exterior Angles
Understand how to extend sides of a polygon to define and label corresponding interior and exterior angles.
00:01:20 - 00:01:49 | Drawing Parallel Lines for Angle Construction
Step-by-step guide to constructing parallel lines that help identify corresponding and alternate angles.
00:01:49 - 00:03:12 | Using Angle Concepts to Fix Exterior Angles
Discover how alternate, corresponding, and opposite angles relate to each other when constructing exterior angles.
00:03:12 - 00:03:49 | Fixing Corresponding Angles (B, C, D, E)
Learn how to systematically mark corresponding angles across all sides of a polygon.
00:03:49 - 00:04:30 | Sum of Exterior Angles Equals 360°
Prove that the sum of all exterior angles of any polygon is 360 degrees, regardless of the number of sides.
00:04:30 - 00:06:14 | Analyzing Interior Angles Composition
Understand how interior angles are formed and how they relate to exterior angles within a five-sided polygon.
00:06:14 - 00:07:47 | Calculating Interior Angle Parts with Expressions
Use algebraic relationships and straight-line angle sums (180°) to express interior angles in terms of exterior ones.
00:07:47 - 00:08:43 | Simplifying Interior Angle Sum Expressions
Simplify and combine expressions to establish relationships between interior and exterior angles.
00:08:43 - 00:10:21 | Factoring Angle Sums and Verifying Formulas
Apply algebraic factorization to confirm that the sum of exterior angles = 360°.
00:10:21 - 00:11:55 | Deriving the Formula for Sum of Interior Angles
Learn how to derive the universal formula:
👉 Sum of Interior Angles = (n – 2) × 180°
00:11:55 - 00:12:35 | Summary of Interior and Exterior Angle Sums
Final recap of both formulas with examples of n-sided polygons.
00:12:35 - 00:13:32 | Channel Promotion & Upcoming Videos
Preview of upcoming lessons on interior angles of polygons, plus playlists on Matrices, Trigonometry, Mechanics, and Sacred Geometry.

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