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Note, this is for a Symmetrical Star -- all 5 points have the same angle, and all 10 outer sides along the perimeter are equal. QUICK FACTS: The angle in any point (or tip) of the star is 36 degrees. If you bisect the angle in any point (split it in half), each angle is 18 degrees.
- Method 1: A Bug’s Eye View
- First Tries at Both Methods
- Following The Bug
- Elegantly Using The Triangles
- Alternate Triangle Methods
Doctor Rick answered: Here is one turn: For comparison, here is what we would do with a pentagon: At each corner the bug turns, ultimately making exactly one complete turn in a circle. So the sum of all the turns is 360°. So what is the sum of the internal angles at those corners? It’s the sum of the supplements of five angles whose sum is 360°; so...
Daniel tried both ways: The rat/bug approach is unclear here; Daniel has probably misunderstood something. The triangle approach is not fully explained here, but upon reading carefully what he says and thinking about what he might be doing, I realize that he may have discovered a very nice way, and found the right answer. And in fact, looking ahead...
Doctor Rick said, It isn’t clear whether this is in fact what Daniel did; but let’s see what he would find if he did (sticking with the bug): It started at A (green) and stopped when it got back to A, without making a final turn; since we don’t know the angles, we can’t know how far it turned. Let’s finish this solution: From the initial direction ...
We’ll see what that meant soon. First, we need a better way to name the triangles: Daniel responded, This Exterior Angle Theorem says that one exterior angle is equal to the sum of the other interiorangles, and is very powerful. This is excellent! Doctor Rick answered: Here is a colored version of his picture to go with the proof: The angle in the ...
I suspect the method Doctor Rick had in mind, using the sum of interior angles of polygons, looked like this: The Exterior Angle Theorem tells us that C’=180^\circ-A-E, and similarly for the other interior angles of the pentagon. A theorem tells us that those angles add up to (n-2)180^\circ, so we can write the equation C’+A’+D’+B’+E’=\\(180-A-E)+(...
Mar 13, 2018 · A regular polygon, like the one that sits in the center of a five pointed star, has equal angles of 108 degrees each. The points of a golden five pointed star are all 36 degrees each, making the other two angles of each point of the star 72 degrees each.
- Jennifer Uhl
A five-pointed star (☆), geometrically an equilateral concave decagon, is a common ideogram in modern culture. Comparatively rare in classical heraldry, it was notably introduced for the flag of the United States in the Flag Act of 1777 and since has become widely used in flags.
Feb 9, 2011 · 86K views 13 years ago. Here's a cute little exercise for students taking a beginning geometry class: Draw a 5-pointed star and discover something interesting about the angles at each of...
- 2 min
- 86.9K
- DrJamesTanton
In this video we see how to find the acute angle x in a 5-pointed regular star using three different methods.For this we review exterior angles, the formula ...
- 9 min
- 5.8K
- The Math District
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How to draw a five-pointed star slideshow. WHAT YOU NEED: Compass, ruler, scissors, pencil and paper. STEP 1 - CIRCLE AND DIAMETER: Draw a circle and a vertical line through its centre. STEP...
