# How Can I Create a Decagon

1. Nov 17, 2014

### 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!

2. Nov 17, 2014

### 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.

3. Nov 18, 2014

### SteamKing

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

4. Nov 18, 2014

### phinds

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

5. Nov 18, 2014

### elegysix

6. Nov 18, 2014

### phinds

7. Nov 18, 2014

### Joffan

Construct a pentagon
Bisect the edges
Draw the decagon.

8. Nov 18, 2014

### DaveC426913

9. Nov 18, 2014

### DaveC426913

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?

10. Nov 18, 2014

### Joffan

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

11. Nov 18, 2014

### DaveC426913

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...

12. Nov 18, 2014

### Joffan

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?

13. Nov 18, 2014

### cenglish

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?

14. Nov 18, 2014

### DaveC426913

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.

15. Nov 18, 2014

### DaveC426913

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

16. Nov 18, 2014

### 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)