Geometry & measures · Angles & polygons
Chapter 1 · 3
The idea
Interior & exterior angles of polygons
Why the exterior angles of any polygon add up to 360°, where (n − 2) × 180° comes from, how regular polygons follow instantly, and the reliable route from a given interior angle back to the number of sides.
A full journey — read it, play with it, work it, then earn real exam marks. Everything stays on the timeline below.
In this lesson — start anywhere
Geometry & measures · Angles & polygons
Interior & exterior angles of polygons
Why the exterior angles of any polygon add up to 360°, where (n − 2) × 180° comes from, how regular polygons follow instantly, and the reliable route from a given interior angle back to the number of sides.
Why it works
Walk round and count the turning
Walk round the polygon and count the turning. Start on one side, walk along it, and at each corner turn through the exterior angle to face along the next side. By the time you arrive back where you started, facing the way you first faced, you have made exactly one full turn. So the exterior angles of any polygon add up to 360° — triangle, hexagon, 100-gon, regular or wildly irregular. The total never depends on .Keep reading — free
The rest of the explanation, plus 2 worked examples you step through move by move.
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