Discover the Sum of Angles in an Irregular Seven Pointed Star - Geometry Proof

  • Thread starter Thread starter msimard8
  • Start date Start date
  • Tags Tags
    Geometry Proof
Click For Summary
SUMMARY

The sum of angles at the tips of an irregular seven-pointed star can be determined by analyzing the geometric properties of the figure. Specifically, one can calculate the total angles formed by the seven triangles and the central septagon, then subtract the angles that do not contribute to the tips of the star. This method involves visualizing the path along the star and counting the complete rotations made, which directly influences the angle sum calculation.

PREREQUISITES
  • Understanding of basic geometric principles, including angles and polygons.
  • Familiarity with the properties of triangles and septagons.
  • Knowledge of rotational symmetry in geometric figures.
  • Ability to visualize and manipulate geometric shapes.
NEXT STEPS
  • Research the properties of irregular polygons and their angle sums.
  • Learn about the relationship between triangles and their angles in complex shapes.
  • Study rotational symmetry and its application in geometry.
  • Explore geometric proofs related to star polygons and their angle calculations.
USEFUL FOR

Students, educators, and geometry enthusiasts seeking to deepen their understanding of angle calculations in complex geometric figures, particularly irregular star shapes.

msimard8
Messages
58
Reaction score
0
Hello, I need help. I need to find a place to start

For the following seven pointed star, detrmine the sum of angles at the tips of the star.

Is there any rule on how to determine the sum of the angles in an irregular star like this one.

Help.
 

Attachments

  • shape.jpg
    shape.jpg
    4.9 KB · Views: 589
Physics news on Phys.org
Try adding up every angle in sight (ie, those making up the 7 triangles and the septagon) and then subtracting the angles you don't want.
 
The total angles in the figure that StatusX is talking about: imagine walking along the figure making the turn at each angle: you wind up facing exactly the way you originally were. How many times do you make a complete rotation?
 

Similar threads

Hyperbolic Geometry (Rectangles)
  • · Replies 1 ·
Replies
1
Views
2K
Suggestions for HS geometry book (proofs)
  • · Replies 14 ·
Replies
14
Views
2K
Using Euler's formula to prove trig identities using "sum to product" technique
  • · Replies 4 ·
Replies
4
Views
2K
What is the sum of interior angles in a hyperbolic n-gon?
  • · Replies 7 ·
Replies
7
Views
2K
Proofs in analytic geometry and vector spaces.
  • · Replies 1 ·
Replies
1
Views
1K
Another trick with Blender using geometry nodes
  • · Replies 1 ·
Replies
1
Views
667
Proving well ordering principle from Peano Axioms
  • · Replies 9 ·
Replies
9
Views
2K
Hyperbolic triangles proof help?
  • · Replies 4 ·
Replies
4
Views
2K
Undergrad J0524-0336, surprisingly high Li concentration
  • · Replies 2 ·
Replies
2
Views
3K
Discover the Length of a Sidereal Day with Just a Star and Time Measurements
  • · Replies 5 ·
Replies
5
Views
2K