Quandaries and Queries


How do you find the measure of interior and exterior angles of a regular polygon when you are given the number of sides?


Hi Aaron,

There are a number of ways to approach this, such as chopping it up into triangles from the central point, and adding angles from the triangles.

However, the simplest way is the following:
- the sum of the exterior angles for any simple (non-intersecting) polygon is 360 degrees. (Basically, the exterior angles measure how much you turn as you walk around the polygon. The total answer is - one full turn or 360 degrees!)

Now, if you have a regular polygon with k vertices (and edges) each of the exterior angles is 360/k. The interior angles can be found by subtracting the exterior angle from a straight line (180 degrees).

So, for an equilateral triangle we have 360/3 = 120 degrees as the exterior angle, and 180-120 = 60 degrees as the interior angle.

For a square, you get 360/4 = 90 degrees as the exterior angle and 180-90 = 90 degrees as the interior angle.

These are values you already know - but it is good to check your formula first.

Now you are ready for any polygon!

Walter Whiteley
York University


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