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60degreesI want to build hexagonal garden beds from 2x6 PT,what angle should i cut? each side will be 24"

Tom

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JackM

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Jack

JackM

The internal angle is 120 therefore the angle to cut is 60

Tom

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Tom's right here guys, but before I explain why...how many times did this op post this question and have they been back to respnd???Jack

The internal angle is 120 therefore the angle to cut is 60

Tom

Here's why:

The least number of sides on a polygon is 3 (triangle). In any triangle, the sum of all angles must equal 180 degrees. Now, every time another side is added, you must add another 180 degrees. So for a rectangle it's 180 + 180 = 360, and since it's 4 sided, 360/4=90 and half of 90 = 45 degrees for the miter.

Now, a hexagon is a 6 sided polygon, so that's 180 + 540 (180 * 3) = 720. So, the sum of all angles in a hexagon must equal 720 degrees. 720/6=120 and half of 120 = 60 degrees for the miter.

If you think about it it makes sense, look at how the angles get larger with the addition of sides:

Equalateral triangle: each angle = 60 degrees

Rectangle/Square: each angle = 90 degrees

Pentagon: each angle = 108 degrees

Hexagon: each angle = 120 degrees

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Real: In any polygon there are only 360 degrees. any multiple sided polygon is figured out: 360 divided by the amount of sides:

6 sides = 60 degrees

8 sides = 45

10 sides = 36

etc etc:icon_smile::smile:

JackM

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That's what I was thinking too Jack, but that isn't how it works. I forgot about it until Tom brought it back up again and I started thinking about it. Your calculations above are incorrect. The total degrees of polygons work out like this:Real: In any polygon there are only 360 degrees. any multiple sided polygon is figured out: 360 divided by the amount of sides:

6 sides = 60 degrees

8 sides = 45

10 sides = 36

etc etc:icon_smile::smile:

JackM

Triangle=180 degrees

rectangle=360 degrees

pentagon=540 degrees

hexagon=720 degrees

Think about it, everytime you add another side, each angle has to "open-up" or get larger.

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Jack

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Calculating each interior angle of any polygon is shown in my post above (and is correct).

The problem is that we need to use that angle and subtract it from 180 degrees. This new angle is what we use (divide by 2) to cut a perfect miter.

So, in this case going back to our original hexagon question (where is that op anyhow?) we have 6 sides, which means we have a total of 720 degrees. Divide 720 by number of sides 6 and you get 120. Now you take 180 (which is a straight line) and subtract the 120 from it. We now have 60 left. Divide the 60 by 2 and we have the miter for each joint=30 degrees

Now, just to lay this thing to rest, I made paper patterns and put 30 degree angles on them using my speed square, and voila, perfect hexagon!

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Why make it hard on yourself? On any arrangement of planes where the lengthy of each plane is the same, Divide 360 by the number of planes (sides) and the result is the included angle of each joint. Divide by 2 and that will be your miter setting.

Ed

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WHOO, sorry for the confusion, just trying to make sure the angle of the dangle is perpendicular to the mass of the _ss :laughing:

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JackM

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Real: In any polygon there are only 360 degrees. any multiple sided polygon is figured out: 360 divided by the amount of sides:

6 sides = 60 degrees

8 sides = 45

10 sides = 36

etc etc:icon_smile::smile:

JackM

EDP kinda like this right? :laughing::yes: Then divide by 2 for miter angle

(360/#of sides)/2

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