Find the size of each interior angle of 6 sided regular polygon?

Answer 1

To answer this question, you need to know a few things, which you probably know already:

1. Any two angles formed by a straight line and a line coming off it in any direction will add to 180 degrees.
2. There are 360 degrees in a circle.
3. In a regular polygon, all of the interior angles will be equal. (I'm sure there's no need to tell you what an interior angle is)

Now, if you think about it, in order for the hexagon (in other words, your 6-sided regular polygon; I'm going to call it a hexagon because it's shorter) be complete, the line that forms the outside of it has to go all the way around in a sort of circle. If you imagine that each side of the hexagon extends out in one direction, like a pinwheel, then the total of those small outside angles is 360 degrees.

There are 6 of those angles, so 360 divided by 6 gives 60 degrees per Exterior Angle in a hexagon.

Now, notice that there is one of these Exterior Angles per Interior Angle, and that the two add to 180 degrees (for the reasons stated above).

So, 180 minus 60 gives 120 degrees per interior angle!

This method works for all regular polygons. There is another method as well: The total of the interior angles in a triangle is 180 degrees. Pick one vertex (corner) of the polygon and draw lines from it to all the other vertices. Count the number of triangles you see, and multiply that number by 180. This gives you the sum of the interior angles in that polygon. Then, if it's regular, divide by the number of interior angles to give you the value of each interior angle.

Remember that both of these methods only work when the polygon is regular.

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