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Interior angles don't have to add to 360. Exterior angles do. For a pentagon, interior angle is 108, exterior angle is 180-108 = 72.

5 * 72 = 360

Tom Veatch Wichita, KS USA

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.

CHRIS

circle

as

Which causes the saw to cut at an angle of (90 - 36) = 54 degrees.

Think about it: what do you set your miter gauge at to make a cut at 90 degrees? Unless you have a really unusual miter gauge, you'll set it at zero.

I think the confusion arises from careless use of terminology.

For***any*** closed polygon of n sides, the sum of the exterior angles is
(n - 2) *** 180
and the measurement at each angle of a regular polygon is
(n - 2) *** 180* / n.
To cut a mitered frame in the shape of a regular polygon of n sides, the
angles at each end of each piece are
(n - 2) * 180 / *(2n).

However, to cut a board at the angle p, one must set the miter gauge to (90 - p) because miter gauges measure angle from a line***perpendicular*** to the edge of
the board being cut. For example, to cut a board square (90 degrees), you set
the miter gauge at zero.

So....

To cut a mitered frame in the shape of a regular polygon of n sides, the _miter_gauge_ setting is (90 - p) where p is (n - 2) * 180* / (2n), or
90 - [(n - 2) * 180 / *(2n)]
simplifying...
= 90 - [(180n - 360)* / (2n)]
= 90 - [(180n / *2n) - (360 / 2n)]
= 90 - [90 - 180/n]
= 180/n

Thus, to cut a mitered frame in the shape of a regular pentagon (n = 5), the _miter_gauge_ setting is 180/5 = 36 degrees. Which produces a 54-degree angle.

-- Regards, Doug Miller (alphageek-at-milmac-dot-com)

For a copy of my TrollFilter for NewsProxy/Nfilter, send email to autoresponder at filterinfo-at-milmac-dot-com

Yet the story continues.... ;-)

You've now got five isosceles triangles (two equal length sides). The angle at the apex is 72 degrees as you noted. Since the sum of the angles of any triangle must be 180 degrees, this leaves 180 - 72 = 108 degrees for the other two angles of each triangle.

Since the other two angles are equal, they must each be 108/2 = 54 degrees. This is the angle between an outside face and the mitre cut's face.

To cut this 54 degree angle on a mitre saw, set the saw to 90 - 54 = 36 degrees, since the saw's scale has 0 degrees as a right angle, and measures deflection from the perpendicular.

It's bang on, in fact.

An octagon can take another turn if you draw a square within a square at 45. Then it's easy to see the inside angle of the octagon as 135. So two cuts would each be 67.5 as you say.

Using the formula:

Each inside angle is (8-2)*180 / 8 = 3/4 of 180 = 135 ...etc.

Dan.

LOL.... I would like to see the 54 degree setting on the saw... I think what the OP was really wanting to know was what to set the saw at.

#### Site Timeline

- posted on April 19, 2004, 2:52 am

Interior angles don't have to add to 360. Exterior angles do. For a pentagon, interior angle is 108, exterior angle is 180-108 = 72.

5 * 72 = 360

Tom Veatch Wichita, KS USA

- posted on April 18, 2004, 8:17 pm

CHRIS

circle

as

- posted on April 18, 2004, 6:56 pm

18°

Bob S.

am

Bob S.

am

- posted on April 18, 2004, 7:13 pm

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

Chris

am

Chris

am

- posted on April 18, 2004, 7:17 pm

360 deg / 5 = 72 deg

Divide in 2 for each side of planter 72 deg /2 = 36 deg at each end of 2x4's.

Graham

am

Divide in 2 for each side of planter 72 deg /2 = 36 deg at each end of 2x4's.

Graham

am

- posted on April 18, 2004, 9:39 pm

In rec.woodworking

WRONG!

And I'll accept your apology anytime you're ready.

WRONG!

And I'll accept your apology anytime you're ready.

- posted on April 18, 2004, 11:35 pm

If I was wrong then I'd apologise, as I'm not, then I won't.

The OP asked "What degree would I need to cut the 2x4's"

He would need to set his compound miter saw to 36 degrees...

Graham

wrote:

The OP asked "What degree would I need to cut the 2x4's"

He would need to set his compound miter saw to 36 degrees...

Graham

wrote:

- posted on April 18, 2004, 11:52 pm

I agree Graham you are NOT wrong. And some people should learn to read the
OP and not jump in the middle of a conversation you should check the posts
on the A.B.P.woodworking about this topic also seems like this post really
opened a can of worms

wrote:

wrote:

- posted on April 18, 2004, 11:57 pm

"Chris Melanson" wrote in message

Hey ... at least it is ON TOPIC!

Hey ... at least it is ON TOPIC!

--

www.e-woodshop.net

Last update: 4/13/04

www.e-woodshop.net

Last update: 4/13/04

Click to see the full signature.

- posted on April 19, 2004, 12:05 am

Which causes the saw to cut at an angle of (90 - 36) = 54 degrees.

Think about it: what do you set your miter gauge at to make a cut at 90 degrees? Unless you have a really unusual miter gauge, you'll set it at zero.

I think the confusion arises from careless use of terminology.

For

However, to cut a board at the angle p, one must set the miter gauge to (90 - p) because miter gauges measure angle from a line

So....

To cut a mitered frame in the shape of a regular polygon of n sides, the _miter_gauge_ setting is (90 - p) where p is (n - 2) * 180

Thus, to cut a mitered frame in the shape of a regular pentagon (n = 5), the _miter_gauge_ setting is 180/5 = 36 degrees. Which produces a 54-degree angle.

-- Regards, Doug Miller (alphageek-at-milmac-dot-com)

For a copy of my TrollFilter for NewsProxy/Nfilter, send email to autoresponder at filterinfo-at-milmac-dot-com

- posted on April 19, 2004, 12:54 am

As I previously stated, read what the OP has asked for, not what you think
he has asked for. If he has asked the wrong question, then that is a totally
different matter.

Bob is not asking what angle his 2x4 has to be cut to (which is 54 deg), he is asking what angle does he "need" to cut the wood, so he can build a 5 sided planter. He needs an angle of 36 deg.

He applies an angle of 36 degrees to his CMS and will be able to build a 5 sided planter.

Graham

wrote:

zero.

of

set

the

angle.

Bob is not asking what angle his 2x4 has to be cut to (which is 54 deg), he is asking what angle does he "need" to cut the wood, so he can build a 5 sided planter. He needs an angle of 36 deg.

He applies an angle of 36 degrees to his CMS and will be able to build a 5 sided planter.

Graham

wrote:

zero.

of

set

the

angle.

- posted on April 20, 2004, 12:20 pm

You guys are making this way too complicated. I'd love to get this
group together to play 'telephone'.

Some careless use of terminology has muddied the picture here. The idea of 'interior' and 'exterior' angles is just confusing. There is only one angle one needs to be concerned with, and that is the (bevel angle) between the center of a regular polygon and any vertex.

The answer to the original question should be obvious by drawing a circumscribed circle about the polygon. Then draw 'spokes' from the center to each vertex. You will have created a bunch of triangles as well as circle segments. As we know from fifth grade math class, the sum of the angles of all circle segments always adds up to 360 degrees. This is the only thing that always adds up to 360 degrees. The sum of the perimeter angles between the polygon segments does not add up to 360 degrees except for 4-sided polygons.

So, with your little sketch, note that the angle between the vertexes and the center of a pentagon is 72 degrees, which also happens to be 360/5. Since your segment includes two such bevel angles, each is 36 degrees. This is the bevel angle. Period. End of story.

Imagine what would have happened if the original poster had wanted to build a gazebo...

Nice to see everybody staying on topic, though...

John

On Mon, 19 Apr 2004 00:05:47 GMT, snipped-for-privacy@milmac.com (Doug Miller) wrote:

John Paquay snipped-for-privacy@insightbb.com

"Building Your Own Kitchen Cabinets" http://home.insightbb.com/~jpaquay/shop.html ------------------------------------------------------------------ With Glory and Passion No Longer in Fashion The Hero Breaks His Blade. -- Kansas, The Pinnacle, 1975 ------------------------------------------------------------------

Some careless use of terminology has muddied the picture here. The idea of 'interior' and 'exterior' angles is just confusing. There is only one angle one needs to be concerned with, and that is the (bevel angle) between the center of a regular polygon and any vertex.

The answer to the original question should be obvious by drawing a circumscribed circle about the polygon. Then draw 'spokes' from the center to each vertex. You will have created a bunch of triangles as well as circle segments. As we know from fifth grade math class, the sum of the angles of all circle segments always adds up to 360 degrees. This is the only thing that always adds up to 360 degrees. The sum of the perimeter angles between the polygon segments does not add up to 360 degrees except for 4-sided polygons.

So, with your little sketch, note that the angle between the vertexes and the center of a pentagon is 72 degrees, which also happens to be 360/5. Since your segment includes two such bevel angles, each is 36 degrees. This is the bevel angle. Period. End of story.

Imagine what would have happened if the original poster had wanted to build a gazebo...

Nice to see everybody staying on topic, though...

John

On Mon, 19 Apr 2004 00:05:47 GMT, snipped-for-privacy@milmac.com (Doug Miller) wrote:

John Paquay snipped-for-privacy@insightbb.com

"Building Your Own Kitchen Cabinets" http://home.insightbb.com/~jpaquay/shop.html ------------------------------------------------------------------ With Glory and Passion No Longer in Fashion The Hero Breaks His Blade. -- Kansas, The Pinnacle, 1975 ------------------------------------------------------------------

- posted on April 20, 2004, 1:40 pm

Yet the story continues.... ;-)

You've now got five isosceles triangles (two equal length sides). The angle at the apex is 72 degrees as you noted. Since the sum of the angles of any triangle must be 180 degrees, this leaves 180 - 72 = 108 degrees for the other two angles of each triangle.

Since the other two angles are equal, they must each be 108/2 = 54 degrees. This is the angle between an outside face and the mitre cut's face.

To cut this 54 degree angle on a mitre saw, set the saw to 90 - 54 = 36 degrees, since the saw's scale has 0 degrees as a right angle, and measures deflection from the perpendicular.

- posted on April 20, 2004, 11:37 pm

On Tue, 20 Apr 2004 09:40:53 -0400, "Greg Neill"

"Building Your Own Kitchen Cabinets" http://home.insightbb.com/~jpaquay/shop.html ------------------------------------------------------------------ With Glory and Passion No Longer in Fashion The Hero Breaks His Blade. -- Kansas, The Pinnacle, 1975 ------------------------------------------------------------------

"Building Your Own Kitchen Cabinets" http://home.insightbb.com/~jpaquay/shop.html ------------------------------------------------------------------ With Glory and Passion No Longer in Fashion The Hero Breaks His Blade. -- Kansas, The Pinnacle, 1975 ------------------------------------------------------------------

- posted on April 20, 2004, 3:14 pm

wrote:

Not quite! You said.... "angle between the vertexes and the center of a pentagon is 72 degrees", which is quite correct. However, that is not the angle in question. The angles being cut are at the vertex, not the center. The angle at the center,subtracted from the triangle [180 degrees] formed by that and the angles at the vertices makes them each half of 180 - 72, or 108/2 = 54 degrees. Two cuts together form the angle at the vertex, 108 degrees.

By the way, has anyone here made those cuts, or made the item in question? It's not too difficult to do with a few scraps.

Dan.

Not quite! You said.... "angle between the vertexes and the center of a pentagon is 72 degrees", which is quite correct. However, that is not the angle in question. The angles being cut are at the vertex, not the center. The angle at the center,subtracted from the triangle [180 degrees] formed by that and the angles at the vertices makes them each half of 180 - 72, or 108/2 = 54 degrees. Two cuts together form the angle at the vertex, 108 degrees.

By the way, has anyone here made those cuts, or made the item in question? It's not too difficult to do with a few scraps.

Dan.

- posted on April 20, 2004, 11:49 pm

It's bang on, in fact.

An octagon can take another turn if you draw a square within a square at 45. Then it's easy to see the inside angle of the octagon as 135. So two cuts would each be 67.5 as you say.

Using the formula:

Each inside angle is (8-2)*180 / 8 = 3/4 of 180 = 135 ...etc.

Dan.

- posted on April 21, 2004, 2:09 am

"Danny Boy" wrote in message

it

You're preaching to the choir! ;>)

it

You're preaching to the choir! ;>)

- posted on April 18, 2004, 11:51 pm

No, that is correct.

wrote:

wrote:

- posted on April 19, 2004, 12:55 am

This all comes down to a matter of where one is measuring the angle from.
Where would the man set his miter saw? 36 dregrees (I almost wrote %%D).

wrote:

wrote:

- posted on April 19, 2004, 1:19 am

LOL.... I would like to see the 54 degree setting on the saw... I think what the OP was really wanting to know was what to set the saw at.

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