Here’s my little buddy, the Slow Turtle. He’s slow, sure—but also determined. And he’s about to show us why, for any polygon, the sum of the exterior angles is always 360 degrees.
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Slow Turtle starts walking along the edge of a polygon. As long as he can feel the side of the shape out to his left, he’s happy. But when he hits a corner—uh oh—he can’t feel anything. So he slowly turns until the shape is on his left again. He does this at every corner, carefully turning to stay in contact.
Eventually, he makes it all the way around the figure. And here’s the key: no matter what kind of polygon it is, he’s made exactly one full turn. That’s 360 degrees of rotation—just distributed over however many corners the shape has.
If you bring those little turns (those exterior angles) back to the center, you’ll see they form a full circle.
That’s why the sum of the exterior angles of any polygon—triangle, hexagon, whatever—is always 360°. The Slow Turtle proves it every time.
#MathExplained #GeometryVisualized #IntuitiveGeometry
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