David W. answered • 11/02/17

Experienced Prof

In the 1960's, Seymour Papert and his team at M.I.T. invented a computer-controlled "turtle" that could draw on paper on the floor. Turtle Graphics is still a great way to explore Geometry.

If a turtle starts facing East and turns and turns and turns and ... turns and ends up at the starting point facing in the same direction as when it started, it has turned 360°. In Geometry, we say,

**"The sum of the external angles is 360°."**Now, a 24-sided regular polygon has 24 turns, each with an external angle of 360°/24, right?

And, each interior angle is

**180° - (360°/24**) because the turtle doesn't go back the way it came, but it turns a angle that is the**supplement**of the exterior angle ["Two angles are supplementary if their angles add up to 180".]Thus, there is a formula for the internal angle of a regular n-sided polygon:

180° - 360°/n

(n-2)*180°/n