Regular heptagon, finding value of unknowns

AI Thread Summary
To find the unknown angles in a regular heptagon, the interior angle is calculated as 128.57 degrees, derived from the formula (n-2)*180/n. The discussion suggests focusing on smaller components, such as the triangle formed at the top of the heptagon, to simplify the problem. Participants are encouraged to identify known angles within that triangle to aid in determining the unknowns. Understanding the relationship between the angles in the triangle and the interior angle of the heptagon is crucial for solving the problem. This approach can effectively lead to finding all unknown angles in the heptagon.
Frank212
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Homework Statement


bandicam 2016-08-14 13-44-31-309.jpg


Homework Equations


(n-2)*180[/B]

The Attempt at a Solution


11.a: 7-2=5, 5*180= 900. 900/7= 128.57 degrees
b. How do you find the unknowns?[/B]
 

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Frank212 said:
How do you find the unknowns
It may help to concentrate on one small piece. Look at the triangle at the top.
 
haruspex said:
It may help to concentrate on one small piece. Look at the triangle at the top.
How do I use 128.57 degrees to help me find the unknowns?
 
Frank212 said:
How do I use 128.57 degrees to help me find the unknowns?
Do you know any of the angles in the top triangle?
 
I picked up this problem from the Schaum's series book titled "College Mathematics" by Ayres/Schmidt. It is a solved problem in the book. But what surprised me was that the solution to this problem was given in one line without any explanation. I could, therefore, not understand how the given one-line solution was reached. The one-line solution in the book says: The equation is ##x \cos{\omega} +y \sin{\omega} - 5 = 0##, ##\omega## being the parameter. From my side, the only thing I could...

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