Find the measure of an interior angle and an exterior angle of each regular polygon

Question

A 24 gon

Is what we have to find the interior and exterior angle of .

Answer 1

In the 1960s, Seymour Papert and his team at MIT developed "Turtle Graphics" -- a device that drew on a flat surface. Today, Turtle Graphics software is free online.

When the Turtle did a series of moves of constant length, it turned the external angle each time and ended up at the original spot facing in the original direction. Thus, the sum of the external angles is 360°.

This makes it easy to find the internal angle of a regular n-gon, because each interior angle is the supplement of the external angle (180ˆ - ext).

So, a regular octagon (8 sides) has an external angle of 360/8 = 45ˆ and an interior angle of 180ˆ-45ˆ= 135°.

Now, when you use the general formulas, they should make more sense.