Tuesday, October 22, 2013


Interior Angles of a Regular Polygon


As we've seen with the (n-2)180 formula, the sum total of the measures of the interior angles of a polygon can be quickly ascertained. Further, each individual measure within can also be ascertained by dividing the sum total by the actual number of sides (n), as long as the polygon is regular.
As per the image above, the more sides of a regular polygon, the closer the shape comes to being a circle. With that, the interior angles are ever increasing towards a max possible value. So if instead of a decagon drawn inside that circle, I drew a 50-sided shape, it would be near impossible to see the shape inside the circle.
So three questions:
1) What is that max value the interior angle measures are approaching as you increase the number of sides?
2) Give an example of the measure of each interior angle of a (you choose)-sided regular polygon. 
3) What is the sum of the measures of the exterior angles of the polygon you've chosen?

My example for #2:
A 45-sided regular polygon has interior angle measure 172 degrees, because [(n-2)*180]/n gives 172 in my case. 

*You must choose a number that no other student has previously chosen and put into the comment section; shouldn't be a problem, as there are an infinite amount of numbers to choose from, so make sure by looking at the other examples. In addition, the number you choose must be greater than any named or previously discussed polygons. Also, if you can manage to choose a number that gives a whole number value (non-decimal) as the interior angle measure, bonus. First come, first serve with that.*


Posted by at

55 comments:

  1. AnonymousOctober 28, 2013 at 7:07 PM

    1. 180
    2. I chose a 20 sided regular polygon. The interior angles measure at 162 degrees.
    3. The exterior angle measures sum to 3,960 degrees.

    ReplyDelete
    Replies
    1. MrletterNovember 2, 2013 at 12:35 PM

      I was looking for the sum of the measures of the exterior angles with #3, but otherwise good. And bonus for 20-sided.

      Delete
  2. AnonymousOctober 29, 2013 at 1:01 PM

    The max value the interior angle measure of side at you increase the number of sides is 180. I chose a 18 sided regular polygon. The interior angle measure (18-2)*180= 2880/18=160 degrees. The exterior angle measure 180 - 160 = 20 degrees.

    ReplyDelete
    Replies
    1. MrletterNovember 2, 2013 at 12:37 PM

      The sum of the exteriors for #3.
      Good job with 18-sided. Bonus.

      Delete
  3. AnonymousOctober 29, 2013 at 4:50 PM

    1) The maximum value of the interior angle measures is 180°.
    2) I chose a 30 sided regular polygon. The interior angle measure of the polygon is 168°.
    3) The exterior angle measure is 12°.

    ReplyDelete
    Replies
    1. MrletterNovember 2, 2013 at 12:39 PM

      Good with 30 for bonus, but #3 called for sum of exterior.

















      Delete
  4. AnonymousOctober 29, 2013 at 5:08 PM

    1. 180
    2. I choose 24 sided regular polygon
    - 22 x 180= 3,960
    - 3,960/24= 165
    3. The exterior angle is 15

    ReplyDelete
    Replies
    1. MrletterNovember 2, 2013 at 12:39 PM

      good with 24-sided, but looking for the sum of the exteriors with #3.

      Delete
  5. AnonymousOctober 29, 2013 at 5:46 PM

    1) The most that the interior angle can measure up to is 180°
    2) I chose a 36 sided regular polygon,
    (36-2)*180/36=170°
    3) This means that the exterior angle is 180°-170° =10°

    ReplyDelete
    Replies
    1. MrletterNovember 2, 2013 at 12:39 PM

      Bonus for 36-sided, but needed the sum of the exteriors.

      Delete
  6. UnknownOctober 29, 2013 at 7:13 PM

    1.180
    2.i chose a 32 sided regular polygon
    (32-2)x180/32=169
    3.the exterior angle is 11

    ReplyDelete
    Replies
    1. MrletterNovember 2, 2013 at 12:40 PM

      Good job with 32-sided, but needed the sum of the exteriors.

      Delete
  7. AnonymousOctober 29, 2013 at 8:39 PM

    1. 180
    2. I choose a 40 sided regular polygon
    [(40-2x180/40=171)] *this actually turned out to be a whole number
    3. Exterior angle is 9

    ReplyDelete
    Replies
    1. MrletterNovember 2, 2013 at 12:40 PM

      Gotta love the whole number hit, but needed the sum of the exteriors.

      Delete
  8. BurkleOctober 30, 2013 at 9:25 AM

    This comment has been removed by the author.

    ReplyDelete
  9. UnknownOctober 30, 2013 at 3:46 PM

    1.180
    2.60 sided regular polygon
    (60-2)*180/40=174
    3.exterior angle=6

    ReplyDelete
  10. AnonymousOctober 30, 2013 at 8:31 PM

    1) 180
    2) 15 sided regular polygon
    (15-2)180/15= 156
    3) the exterior angle is 24

    ReplyDelete
  11. AnonymousOctober 31, 2013 at 1:30 PM

    Tim Kostoff
    1) 180
    2) 72 sided regular polygon
    n-2(180)= sum of interior angles
    72-2(180)=12600
    72-2(180)/72=175
    3)180-175=5
    5*72=360

    ReplyDelete
    Replies
    1. MrletterNovember 2, 2013 at 12:42 PM

      Yay!! You stated the sum of the exteriors! Nicely done.

      Delete
  12. AnonymousOctober 31, 2013 at 4:34 PM

    1)180
    2)7
    3) (7-2)180=900
    900/7=128.57

    ReplyDelete
    Replies
    1. MrletterNovember 2, 2013 at 12:43 PM

      Question #3 asked for the sum of the exteriors.

      Delete
  13. UnknownOctober 31, 2013 at 4:40 PM

    1) 180
    2) 47 sided polygon
    3) (47-2)180=8100
    4) 8100/47=172.34

    ReplyDelete
  14. AnonymousOctober 31, 2013 at 5:25 PM

    1)180
    2)9
    3)Exterior angle is 140

    ReplyDelete
    Replies
    1. MrletterNovember 2, 2013 at 12:44 PM

      Don't understand what you meant by'9' for #2, and the sum of the exteriors is 360.

      Delete
  15. AnonymousNovember 1, 2013 at 7:04 AM

    1.180
    2.360-2*180=64440
    64440/360=179

    ReplyDelete
    Replies
    1. MrletterNovember 2, 2013 at 12:45 PM

      Good job on hitting 179. Needed the sum of the exteriors also, though.

      Delete
  16. AnonymousNovember 1, 2013 at 7:14 AM

    1.180
    2.34
    3.34-2(180) = 5760
    4.5760 / 34=169.4

    ReplyDelete
  17. chris cosenzaNovember 1, 2013 at 11:00 AM

    1. 180
    2. 20 sided polygon
    3. 20-2(180)=3240

    ReplyDelete
    Replies
    1. MrletterNovember 2, 2013 at 12:46 PM

      Someone above you did a 20-sided polygon. You can choose any number that hasn't already been used by another student above basically 12. Infinite choices.

      Delete
  18. AnonymousNovember 1, 2013 at 11:03 AM

    180
    20
    (20-2)180=3240
    3240/34=95.2

    ReplyDelete
    Replies
    1. MrletterNovember 2, 2013 at 12:47 PM

      Someone above you 20-sided already. Should've chosen a different # of sides.

      Delete
  19. AnonymousNovember 1, 2013 at 3:01 PM

    1. 180
    2. 52 sides of polygon
    (52-2)*180/52=173.076923
    3. 360

    ReplyDelete
  20. UnknownNovember 3, 2013 at 9:28 AM

    1. 180
    2. 30 sided regular polygon
    3. (30-2)180=5040
    (30-2)180=5040/30=168
    4.180-168=12
    5. 5*30=150

    ReplyDelete
  21. UnknownNovember 3, 2013 at 11:21 AM

    1. 180
    2. 55 sided regular polygon
    3. (55-2)180= 9,540

    ReplyDelete
  22. UnknownNovember 3, 2013 at 12:59 PM

    1. 180
    2. 65 sided Regular Polygon
    3. (65 -2)180= 11,340

    ReplyDelete
  23. AnonymousNovember 3, 2013 at 6:15 PM

    1. 180
    2. (33-2)180/33= 5,580
    3.10.9

    ReplyDelete
  24. AnonymousNovember 4, 2013 at 5:45 PM

    180
    (42-2)180/42=180
    360

    ReplyDelete
  25. UnknownNovember 5, 2013 at 5:04 PM

    1. 180
    2. 62 sided regular polygon
    3. (62-2)180/62 = 174.2

    ReplyDelete
  26. UnknownNovember 6, 2013 at 9:08 AM

    1. 180
    2. (44-2)180= 7560
    (44-2)180/44= 171.8
    3. 180- 171.8= 8.2
    44(8.2)=360.8

    ReplyDelete
  27. pcxxmNovember 6, 2013 at 5:44 PM

    1. 180 - It can approach 180 but it can never be 180 because that is a straight line.
    2. I chose a 16 sided shape. Each interior angle was 157.5.
    3. The sum of the exterior angles is 360. The exterior angles of any shape should add to 360 because that inscribes a circle!!!!!!!

    ReplyDelete
  28. AnonymousNovember 7, 2013 at 7:19 PM

    1.180
    2. (80-2)180/80=175.5
    3.360

    ReplyDelete
  29. AnonymousNovember 7, 2013 at 7:22 PM

    1. 180
    2. 55 sided regular polygon
    3. (55-2)180= 9,540

    ReplyDelete
  30. UnknownNovember 8, 2013 at 7:10 AM

    1. 180
    2. 26 sided regular polygon
    3. (26-2)180/26= 6.92

    ReplyDelete
  31. AnonymousNovember 8, 2013 at 1:34 PM

    1. 180
    2. 6 sided polygon
    3.(4-2)180/4=90

    ReplyDelete
  32. UnknownNovember 8, 2013 at 1:36 PM

    1. 180
    2. 28 sided polygon
    3. (28-2)180/28+=6.428

    ReplyDelete
  33. UnknownNovember 12, 2013 at 7:11 AM

    1.180
    2.10 sided polygon
    3(10-2)180/8=22,.5

    ReplyDelete
  34. OliviaRNovember 12, 2013 at 3:42 PM

    1. 180
    2. 5 sides
    3. (5-2)180/5=108

    ReplyDelete
  35. UnknownNovember 20, 2013 at 5:18 PM

    1. 180
    2. 72 sided shape
    3. (72-2)180/72 = 175

    Keelie

    ReplyDelete
  36. AnonymousDecember 4, 2013 at 6:36 PM

    1:180
    2:30 sided shape
    3: (30-2)180/30 Answer: 168

    ReplyDelete
  37. AnonymousDecember 16, 2013 at 8:38 AM

    1.) 180
    2.) 26 sided REGULAR polygon
    3.) (10-2)18018=22.5

    ReplyDelete

Subscribe to: Post Comments (Atom)