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Why Does Every Polygon's Exterior Angles Add Up to 360º? The Slow Turtle Knows!

Check out the main channel ‪@polymathematic‬ There's a nifty little formula for the sum of the measures of the interior angles of a polygon, but what about the exterior angles. Is there a simple way to compute the sum of the measures of the exterior angles for a polygon of n sides or corners? We can actually do even better than a formula. We have the answer! It turns out the sum of the measures of the exterior angles of a simple polygon is 360º no matter how many sides it has. To understand why, let's turn to a very determined, very slow turtle. The slow turtle helps us think through what's happening at each exterior angle, regardless of the specifics of the polygon. The slow turtle will walk along the outside of the polygon, hugging the edge until he gets to each next corner. Then he'll turn just enough to get back to hugging the edge and begin walking forward again. By the time the slow turtle gets back to where he started, regardless of how many times he had to stop and turn, he will have made one full revolution. Therefore, the sum of the measures of the exterior angles of a polygon will always be 360º. #theslowturtle #ExteriorAngleSum #GeometryInsights Follow Tim Ricchuiti: TikTok:   / polymathematic   Mathstodon: https://mathstodon.xyz/@polymathematic Instagram:   / polymathematicnet   Reddit:   / polymath-matic   Facebook:   / polymathematic   Watch more Math Videos: Math Minis:    • Math Mini   Math Minutes:    • Math Minutes   Number Sense:    • Number Sense (UIL / PSIA)   MATHCOUNTS:    • MATHCOUNTS