How to Construct a Decagon Using a Protractor and Compass

[cenglish]

Hi guys, I have been working for a long time and have attempted to construct a decagon but have failed all three times. I know that all the external angles are 144 degrees and they all add up to 1440 degrees. Every time I draw the decagon I come up with a hendecagon. I don't know why I come up with this because I have all of the angles that a decagon consist of. I have searched up YouTube videos on how to create a decagon, but none of them seem to help. I would appreciate if someone could suggest a way to construct a proper decagon. Thank You!

 

[phinds]

can't you divide up a circle into 10 equal parts? What would the angle be for each segment? This seems awfully easy unless I'm missing something.

 

[SteamKing]

This is a geometry problem, which does not belong in the Intro Physics HW forum. I'm moving it to the General Math forum.

 

[phinds]

Oh. You have to do this with a compass and a straight-edge?

 

[elegysix]

print this image http://mathworld.wolfram.com/images/eps-gif/Decagon_500.gif
cut it out,
trace it.
win.

 

[phinds]

print this image http://mathworld.wolfram.com/images/eps-gif/Decagon_500.gif
cut it out,
trace it.
win.

This should have been

"cut it out
trace it (cheat)
win"

Besides, this is not a geometric method for the construction and doesn't answer the OP's question.

 

[Joffan]

Construct a pentagon
Bisect the edges
Draw the decagon.

 

[DaveC426913]

Construct a pentagon
Bisect the edges
minor step missing in here.
Draw the decagon.

 

[DaveC426913]

Every time I draw the decagon I come up with a hendecagon.

I think it is pretty apparent that your angles are not 144 degrees then. What kind of protractor are you using? One of those little plastic ones from the dollar store?

 

[Joffan]

minor step missing in here

Actually, I made more steps than needed, not fewer, bisecting being harder than simply drawing a line given two points.

Construct a pentagon which will have an enclosing circle as part of the construction
Find the extra vertices for the decagon on that circle by drawing a diameter from each pentagon vertex
Draw the decagon.

 

[DaveC426913]

Actually, I made more steps than needed, not fewer, bisecting being harder than simply drawing a line given two points.

You can bisect the sides of a pentagon, but that there's still a few steps before you get a decagon from that. Granted, they're not hard steps...

 

[Joffan]

You can bisect the sides of a pentagon, but that there's still a few steps before you get a decagon from that. Granted, they're not hard steps...

Not sure what steps you're talking about that aren't covered by "draw the decagon", simply meaning draw the edges between the already-found vertices.

Unless you have erased the enclosing circle from the pentagon construction? Or drawn the bisectors so short they don't touch the circle?

 

[cenglish]

I think it is pretty apparent that your angles are not 144 degrees then. What kind of protractor are you using? One of those little plastic ones from the dollar store?

Yes, I do use the plastic protractor that is provided for me at my school. Would you suggest going out and buying one of my own?

 

[DaveC426913]

Not sure what steps you're talking about that aren't covered by "draw the decagon", simply meaning draw the edges between the already-found vertices.

Unless you have erased the enclosing circle from the pentagon construction? Or drawn the bisectors so short they don't touch the circle?

It wasn't a given that the construction of the pentagon included an enclosing circle. He could have constructed with just a ruler and protractor.

 

[DaveC426913]

Yes, I do use the plastic protractor that is provided for me at my school. Would you suggest going out and buying one of my own?

No, it's just that your method is fine; it's simply the execution that's flawed.

 

[Joffan]

If you are using a protractor and it's simply an accurate drawing issue:

• Draw your zero line (wider than the intended shape), mark a centre point
• Use compasses to draw the enclosing circle for your decagon
• Put your protractor zero on the zero line at the centre mark
• Check that 0 and 180 are both on the zero line
• Mark points at 36, 72, 108 and 144 degrees
• Draw straight lines (diameters) full across the circle from each marked point through the centre
• Draw the decagon using the intersecting points on the circle (including the intersection with the zero line)
• Remove your construction lines.