My wife would like a 5 sided planter. Just thinks it would look cute?? I am not a wood worker but, have access to a compound miter saw. What degree would I need to cut the 2x4's to achieve this? They will each be 27" long.
It would be a 36 degree angle The way to figure out any angle is very simple you divide 360 by the number of sides then divide your answer in halve to find out your miter example for a square : 360 / 4 = 90 then 90 / 2 = 45 degree angle Example for a pentagon : 360 / 5 = 72 then 72/ 2 = 36 degree angle
The sum of the interior angles of a polygon is (n-2)*180 degrees, where n is the number of sides. Note that this has nothing to do with the _central_ angle of a circle.
In the case of a pentagon, the sum of the interior angles is:
A = (5-2)*180 = 540 degrees
So each of the five interior angles of a regular (all sides the same length) pentagon is 540/5 = 108 degrees.
Equal-angle mitres should be half of this, or 54 degrees.
Ok you go ahead and build it that way and see what you end up with. I will guarantee you do not end up with a pentagon at all not even a square. Use some common sense if you use 45 degrees to get a square how the hell do you come up with 108 degrees?? 108 dose not even divide into 360 evenly you end up with
3.333333333333333333333333333333333 and so on show me a 3.33333333333333333 sided object through the rose coloured glasses you wear. and I will sell you the patent to widgets ok
If you would like the real formula for a MITER it is as follows A=(360/x)/2 where "a" is the MITER "x" is the number of sides For interior or exterior angles it would be A=(360/x) where "A" is the interior or exterior angle.
The one lacking common sense is you Chris. You use 45 to get 90 degree corners in a square. A pentagon has obtuse angles bonehead. Let's bet before you go look at a.b.p.w to see the AutoCAD drawing I posted.
Could you please go and make a pentagon and see for yourself that 36 Degrees will work for a MITER. I have CAD programs (IE Auto CAD V- 7 all the way up to 2004) and do know how to use them. I also am a very experienced cabinetmaker and am more than capable of making SIMPLE MITERS and using common sense. If you want all five sides of a pentagon to be of equal length you would have to use a common MITER of 36 degrees. If you have trouble comprehending that there is no sense even trying to explain it any further. GO MAKE A PENTAGON AND FIGURE IT OUT FOR YOURSELF. Also please knock off your condescending attitude about "Folks are obviously better educated in the UK these days" because you are only making yourself look foolish with your self righteous comments.
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